Use "Matrices" in a sentence | "Matrices" sentence examples

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Matrices is a mathematical term that refers to a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is a fundamental concept in linear algebra and is used in various fields such as physics, engineering, computer science, and economics. If you are struggling to use the word matrices in a sentence, here are some tips to help you:


1. Understand the meaning of matrices: Before using the word matrices in a sentence, it is essential to understand its meaning and context. Matrices are used to represent linear transformations, systems of linear equations, and other mathematical concepts. Knowing the meaning of matrices will help you use it correctly in a sentence.


2. Use matrices in a mathematical context: Matrices are primarily used in mathematical contexts, so it is best to use them in such contexts.

For example, "The solution to the system of linear equations can be found by using matrices."


3. Use matrices in a scientific context: Matrices are also used in scientific fields such as physics and engineering.

For example, "The transformation of a vector can be represented by a matrix in physics."


4. Use matrices in a computer science context: Matrices are used in computer science for various applications such as image processing, machine learning, and computer graphics.

For example, "The image can be transformed using a matrix in computer graphics."


5. Use matrices in an economic context: Matrices are also used in economics for modeling and analyzing economic systems.

For example, "The input-output matrix is used to analyze the interdependence of different sectors in the economy."


6. Use matrices in a sentence with appropriate grammar: When using matrices in a sentence, it is essential to use appropriate grammar.

For example, "The matrices are used to represent the coefficients of the system of linear equations."


7. Use matrices in a sentence with appropriate punctuation: Punctuation is also crucial when using matrices in a sentence.

For example, "The determinant of the matrix is calculated using the formula |A|."


In conclusion, matrices are a fundamental concept in mathematics and are used in various fields such as physics, engineering, computer science, and economics. To use the word matrices in a sentence, it is essential to understand its meaning and context and use appropriate grammar and punctuation. By following these tips, you can use matrices correctly in your writing and communication.


In the remaining portion of this article, additional example sentences are presented to demonstrate the usage of the term "Matrices" within sentences.



Use "matrices" in a sentence | "matrices" sentence examples

"Matrices"

(1) The two matrices are equivalent.

(2) The 'matrices' array is of type object.

(3) The product of two matrices is a matrix.

(4) The 'matrices' array can be multidimensional

(5) Coprime matrices have no common eigenvectors.

(6) Can you explain how to convolve two matrices?

(7) The moduli of the two matrices are different.

(8) The array 'matrices' contains multiple matrices.

(9) The 'matrices' array can be resized dynamically.

(10) Unimodular matrices have determinant equal to 1.



Sentence For "Matrices"

(11) Unimodular matrices play a role in number theory.

(12) CSPs can be represented using graphs or matrices.

(13) The absolute-values of matrices are determinants.

(14) Diagonalizable matrices have distinct eigenvalues.

(15) The 'matrices' array is used to store matrix data.

(16) The commutative property is a property of matrices.

(17) Inverse matrices are denoted by the superscript -1.

(18) Antisymmetric matrices have applications in physics

(19) 'Arrays' can be used to represent matrices or grids.

(20) The codomain of a function can be a set of matrices.



"Matrices" In A Sentence

(21) The computer program multiplieth matrices with ease.

(22) The unitarily equivalent matrices have the same rank.

(23) Idempotents can be used to define idempotent matrices

(24) Unimodular matrices have applications in cryptography.

(25) The unitarily equivalent matrices have the same trace.

(26) The array simplexes can be represented using matrices.

(27) Inverse matrices are only defined for square matrices.

(28) In algebra, we learn to find determinants of matrices.

(29) Pointers can be used to create and manipulate matrices.

(30) The tensor product of two matrices yields a new matrix.




"Matrices" Sentence

(31) We can use arrays to represent matrices in mathematics.

(32) The trigrams can be visualized using graphs or matrices.

(33) Polytopes can be represented using matrices and vectors.

(34) Simultaneous equations can be represented using matrices.

(35) The 'matrices' array can be converted to other data types

(36) APL allows for easy manipulation of matrices and vectors.

(37) Unimodular matrices have a determinant of either 1 or -1.

(38) Linear systems of equations can be solved using matrices.

(39) Linear transformations can be represented using matrices.

(40) The Eigen library supports both dense and sparse matrices.



"Matrices" Sentence Examples

(41) Unimodular transformations can be represented by matrices.

(42) The corresponding entries in these two matrices are equal.

(43) Glycoproteins are commonly found in extracellular matrices.

(44) Unimodular matrices have applications in quantum mechanics.

(45) The math textbook explains how to multiply across matrices.

(46) The two matrices are cogredient with respect to each other.

(47) Algebraically, the two matrices can be added or subtracted.

(48) Inverting matrices without a calculator can be challenging.

(49) Diagonalizable matrices are commonly used in linear algebra.

(50) A linear system can be represented using augmented matrices.



Sentence With "Matrices"

(51) The 'matrices' array can be looped through using a for loop.

(52) The 'matrices' array can be cleared using the splice method.

(53) The unitarily equivalent matrices have the same determinant.

(54) Homopolymers can be used as matrices in composite materials.

(55) The algorithm multiplies matrices to solve complex equations.

(56) The set of all matrices of a fixed size forms a vector space.

(57) The student struggled to multiplicate the matrices correctly.

(58) The computer program can quickly multiplicate large matrices.

(59) The 'matrices' array can be reversed using the reverse method.

(60) The 'matrices' array can be iterated using the forEach method.




Use "Matrices" In A Sentence

(61) Endomorphisms can be represented by matrices in certain cases.

(62) The array boggards can be used to represent matrices or grids.

(63) A linear system can be represented using matrices and vectors.

(64) The 'matrices' array can be initialized with predefined values.

(65) Unitarity is a key property of matrices used in linear algebra.

(66) The unitarily equivalent matrices have the same Frobenius norm.

(67) The linotype operator expertly adjusted the machine's matrices.

(68) The product of two matrices can be found using the dot product.

(69) You can exponentiate matrices as well as numbers and variables.

(70) A square matrix can be partitioned into smaller square matrices.



Sentence Using "Matrices"

(71) The affine combination of two matrices resulted in a new matrix.

(72) The math competition included a section on multiplying matrices.

(73) Unimodular matrices have interesting properties in group theory.

(74) The unitarily diagonalizable matrices have distinct eigenvalues.

(75) The unitarily equivalent matrices have the same singular values.

(76) The unitarily equivalent matrices have the same spectral radius.

(77) The mathematician studied the properties of tetragonal matrices.

(78) The use of matrices is an important tool in analytical geometry.

(79) Unimodular matrices play a key role in the theory of Lie groups.

(80) Unimodular matrices have been extensively studied in mathematics.



Sentences With "Matrices"

(81) The unitarily equivalent matrices have the same condition number.

(82) Nonsymmetric matrices have distinct eigenvalues and eigenvectors.

(83) The mathematician studied symmetric matrices and their properties.

(84) Matrix inversion is not possible for matrices that are not square.

(85) Algebraic equations can be solved using matrices and determinants.

(86) The concept of orthogonal matrices is important in linear algebra.

(87) Fortran is highly efficient in handling large arrays and matrices.

(88) The distributivity of matrices is a key concept in linear algebra.

(89) I have found Eigen to be very efficient in handling large matrices.

(90) The computer program can multiplicate matrices with high precision.



Sentence Of "Matrices"

(91) Unimodular matrices are often encountered in optimization problems.

(92) We can use circulant matrices to solve linear systems of equations.

(93) The 'matrices' array can be sorted using various sorting algorithms.

(94) The isocratic elution mode is preferred for certain sample matrices.

(95) Nilpotent matrices can be used to solve systems of linear equations.

(96) The corresponding entries in these two matrices have the same trace.

(97) The mathematician studied the properties of two-dimensional matrices.

(98) Matrix inversion can be computationally expensive for large matrices.

(99) Isomorphic arrays can be represented as matrices for easier analysis.

(100) The concept of exponentiation can be applied to matrices and vectors.



"Matrices" Sentences

(101) Matrix inversion can be computationally intensive for large matrices.

(102) Accessing elements in the 'matrices' array is done using index values.

(103) Vectors can be represented algebraically using column or row matrices.

(104) Invertible matrices are used in computer graphics for transformations.

(105) Eigenvectors can be calculated for both square and non-square matrices

(106) The equivalence of two matrices can be determined by their dimensions.

(107) The professor explained how to exponentiate matrices in linear algebra.

(108) The algorithm efficiently handles the concatenations of these matrices.

(109) The concept of antisymmetric matrices is widely used in linear algebra.

(110) The mathematician will multiply upon the matrices to solve the problem.



"Matrices" Use In Sentence

(111) Matrix inversion is a key step in calculating determinants of matrices.

(112) The multiplicative property of matrices is essential in linear algebra.

(113) The identity matrix is a building block for constructing other matrices.

(114) He can multiply matrices with ease, but he struggles with basic algebra.

(115) Diagonalizable matrices have a special form that simplifies calculations.

(116) The 'matrices' array can be converted to a heap using heapify operations.

(117) I can easily generate correlation matrices using the statistical package.

(118) The algebraical concept of matrices was introduced in the advanced class.

(119) Circulant matrices have applications in the analysis of time series data.

(120) The 'matrices' array can be joined with a separator using the join method.



Sentence On "Matrices"

(121) Simultaneous equations can be solved using matrices and matrix operations.

(122) The corresponding entries in these two matrices have the same determinant.

(123) Algebraic equations can be solved using elimination, or by using matrices.

(124) The 'matrices' array can be copied to another array using the slice method.

(125) The transpose of a sum of matrices is equal to the sum of their transposes.

(126) The professor explained the concept of orthogonal matrices to the students.

(127) The unitarily equivalent matrices have the same determinant of the adjoint.

(128) The observability of a system can be assessed using observability matrices.

(129) The metric space of square matrices is an example of a non-Euclidean space.

(130) The 'matrices' array can be converted to a string using the toString method.



"Matrices" Example

(131) The 'matrices' array can be checked for emptiness using the length property.

(132) The 'matrices' array can be converted to a set to remove duplicate elements.

(133) Pseudographs can be represented using adjacency matrices or adjacency lists.

(134) The mathematician's theorem proved the existence of diagonalizable matrices.

(135) Circulant matrices can be diagonalized using the discrete Fourier transform.

(136) The determinant of a product of matrices can be found using some properties.

(137) The computer program was designed to diagonalize large matrices efficiently.

(138) Don't forget to multiply out the matrices before adding or subtracting them.

(139) The immunoassays provided reliable results even with complex sample matrices.

(140) The mathematician discovered a new method to diagonalize non-square matrices.



"Matrices" In Sentence

(141) The accuracy of matrix inversion can be affected by ill-conditioned matrices.

(142) The diagonalisation technique is applicable to both real and complex matrices.

(143) Antisymmetric matrices can be used to represent skew-symmetric bilinear forms.

(144) Diagonalisation is a mathematical technique used to simplify complex matrices.

(145) Octonions are often represented using matrices or Cayley-Dickson construction.

(146) Understanding matrices is an important mathematical process in linear algebra.

(147) Circulant matrices have applications in image processing and data compression.

(148) The subspace of a matrix is a set of matrices that satisfy certain conditions.

(149) The linear algebra textbook had a chapter dedicated to diagonalizing matrices.

(150) The unitary group in mathematics is a set of matrices with a determinant of 1.



"Matrices" Sentences In English

(151) In linear algebra, idempotents are matrices that satisfy the equation A^2 = A.

(152) The coefficient matrix is used to study the properties of vectors and matrices.

(153) Pseudographs are often represented using adjacency matrices or adjacency lists.

(154) The array 'corylus' can be used to represent multidimensional data or matrices.

(155) Eulerian graphs can be represented using adjacency matrices or adjacency lists.

(156) Chromatographic separations can be performed on a wide range of sample matrices

(157) The mathematician's research focused on how to diagonalize non-square matrices.

(158) An indecomposable matrix cannot be expressed as a sum of two non-zero matrices.

(159) The commutativity of matrix addition allows us to switch the order of matrices.

(160) The linotype operator carefully selected the metal matrices for each character.



Make Sentence With "Matrices"

(161) The algorithm for solving a system of linear equations involves using matrices.

(162) The process of diagonalising a matrix can be time-consuming for large matrices.

(163) The process of diagonalizing a matrix can be time-consuming for large matrices.

(164) Galactosylated proteins are involved in the formation of extracellular matrices.

(165) Isocratic conditions are not recommended for the separation of complex matrices.

(166) The equivalence of two matrices can be determined by comparing their dimensions.

(167) The group of unimodular matrices is an important object of study in mathematics.

(168) The mathematician proved that orthogonal matrices preserve the length of vectors.

(169) Nilpotent matrices have applications in various areas of science and engineering.

(170) The versatility of gas-chromatography allows for the analysis of complex matrices



Sentences Using "Matrices"

(171) When working with matrices, you may need to exponentiate outside the determinant.

(172) Diagonalizable matrices have distinct eigenvalues with corresponding eigenvectors.

(173) The professor taught us how to exponentiate over matrices in linear algebra class.

(174) Matrix inversion is an essential operation in solving problems involving matrices.

(175) Unimodular matrices have properties that make them useful in various applications.

(176) The commutative law is a property that is applicable to both vectors and matrices.

(177) Matrix multiplication is used in calculating the Hadamard product of two matrices.

(178) Diagonalizable matrices play a crucial role in various applications of mathematics.

(179) Matrix multiplication can only be performed on matrices with compatible dimensions.

(180) The 'matrices' array can be accessed using both positive and negative index values.



Sentence From "Matrices"

(181) The 'matrices' array can be concatenated with other arrays using the concat method.

(182) The 'matrices' array can be sliced to create a new array with a subset of elements.

(183) The 'matrices' array can be converted to a map to associate each matrix with a key.

(184) Vectors can be multiplied by matrices to perform transformations in linear algebra.

(185) Indeterminate equations can be solved using matrices and linear algebra techniques.

(186) The functionalization of carbon fibers improves their adhesion to polymer matrices.

(187) Matrix multiplication is used in calculating the Kronecker product of two matrices.

(188) Glycosylated glycosaminoglycans are important components of extracellular matrices.

(189) The analytical method required the elimination of aqueous matrices from the sample.

(190) When you multiply apart the matrices, you can find the product of the two matrices.

(191) The teacher asked us to multiply matrices as part of our linear algebra assignment.

(192) When you subtract matrices, you need to use matrix addition with the opposite sign.

(193) The process of matrix inversion can be computationally intensive for large matrices.

(194) The detection of colinearity can be done using correlation matrices or scatterplots.

(195) The study of endomorphisms is essential in understanding the properties of matrices.

(196) Solid-phase microextraction can be used for the analysis of various sample matrices.

(197) The peptization of carbon nanotubes allows for their dispersion in polymer matrices.

(198) Diagonalizable matrices have a special property that simplifies their representation.

(199) The 'matrices' array can be converted to JSON format using the JSON.stringify method.

(200) Kakeru is an operation that can be applied to matrices and vectors in linear algebra.

(201) The process of diagonalisation can be applied to both square and non-square matrices.

(202) Idempotents play a crucial role in the theory of matrices and linear transformations.

(203) Galactosylated glycosaminoglycans are important components of extracellular matrices.

(204) The circulant diagonalization property simplifies the analysis of circulant matrices.

(205) Diagonalizable matrices have a unique factorization into eigenvalues and eigenvectors.

(206) The discriminator's output can be visualized using techniques like confusion matrices.

(207) Collinearity can be assessed using correlation matrices or variance inflation factors.

(208) Linear equations can be represented using matrices and solved using matrix operations.

(209) The orthonormality of eigenvectors plays a significant role in diagonalizing matrices.

(210) Chromatometry is a versatile technique that can be applied to various sample matrices.

(211) The monoid of matrices under multiplication is an important concept in linear algebra.

(212) When working with matrices, factorize out any common factors to simplify calculations.

(213) The algebraic sum of two matrices can be found by adding their corresponding elements.

(214) The array trepan can be used to represent multidimensional data structures or matrices.

(215) Cyanoethylated polymers have been used as matrices for controlled drug release systems.

(216) To evaluate accuracy, we can use confusion matrices to analyze the model's performance.

(217) The process of matrix inversion can be simplified using certain properties of matrices.

(218) The comparison operation between the two matrices showed differences in their elements.

(219) Some algebraists study the algebraic properties of matrices and linear transformations.

(220) The 'matrices' array can be reduced using the reduce method to calculate a single value.



Short & Simple Example Sentence For "Matrices" | "Matrices" Sentence

(221) Noncommutative matrices have properties that differ from their commutative counterparts.

(222) The comparison operation between the two matrices showed similarities in their elements.

(223) Serialism often involves the use of matrices to organize pitch and rhythm relationships.

(224) The mathematical concept of antisymmetric matrices is used in various fields of science.

(225) Linear algebra is a branch of mathematics that deals with linear equations and matrices.

(226) Mathematical analysis is used to study the behavior of mathematical vectors and matrices.

(227) Circulant matrices have applications in quantum computing and quantum information theory.

(228) The 'matrices' array can be converted to a stack or a queue using push and pop operations.

(229) The study of random matrices involves analyzing stochastic processes with matrix elements.

(230) The 'matrices' array can be used for mathematical operations such as matrix multiplication.

(231) Antisymmetric matrices have special properties that make them useful in various applications

(232) Orthogonal matrices have many applications in fields such as computer graphics and robotics.

(233) Simultaneous equations can be represented using matrices and solved using matrix operations.

(234) Matroids can be represented using different mathematical models, such as matrices or graphs.

(235) Circulant codes are error-correcting codes that exploit the circulant structure of matrices.

(236) Abstract data types can be used to represent mathematical concepts such as sets or matrices.

(237) The set of all square matrices of a fixed size forms a semigroup under matrix multiplication.

(238) When working with matrices, you may need to exponent out the determinant to find the inverse.

(239) The HPLC method is sensitive enough to detect trace amounts of impurities in complex matrices.

(240) The concept of orthogonal projection is closely related to the concept of projection matrices.



How Do You Write A Good Sentence With "Matrices"?

(241) Multidimensional arrays are useful for representing matrices and other mathematical structures.

(242) The identity matrix is a special type of matrix that preserves the properties of other matrices.

(243) The associative law is a concept that is extended to matrices and other mathematical structures.

(244) The concept of a vector space is foundational in the study of linear transformations and matrices.

(245) The multi-directional array is useful for representing matrices and other complex data structures.

(246) The product of two matrices is found by multiplying the corresponding elements and adding them up.

(247) The determinant of a matrix product is the product of the determinants of the respective matrices.

(248) A matrix is diagonalizable if it can be expressed as a product of diagonal and invertible matrices.

(249) The 'matrices' array can be mapped using the map method to create a new array with modified values.

(250) The incorporation of fluorophosphate into polymer matrices can enhance their mechanical properties.

(251) The multiclass problem can be visualized using confusion matrices to analyze classification errors.

(252) The 'matrices' array can be checked for the presence of a specific matrix using the includes method.

(253) The transpose of a product of matrices is equal to the product of their transposes in reverse order.

(254) Circulant matrices are used in the design of efficient algorithms for solving optimization problems.

(255) The matrix is diagonalizable if it can be expressed as a product of diagonal and invertible matrices.

(256) Circulant matrices are used in the design of efficient algorithms for solving differential equations.

(257) Understanding matrices involves applying a mathematical process to analyze systems of linear equations.

(258) The result of matrix multiplication is a new matrix with dimensions determined by the original matrices.

(259) The result of matrix multiplication can be interpreted as a linear combination of the original matrices.

(260) The associativity of the matrix multiplication determines the order in which the matrices are multiplied.



English Sentences With Audio Using The Word "Matrices".

(261) The 'matrices' array can be filtered using the filter method to create a new array with specific criteria.

(262) Circulant matrices are used in the design of efficient algorithms for solving linear programming problems.

(263) Coulometric titration is a useful technique for analyzing trace amounts of substances in complex matrices.

(264) Antisymmetric matrices have a diagonal of zeros and their entries satisfy the condition A[i][j] = -A[j][i].

(265) Dynamic programming algorithms often involve the use of dynamic data structures such as arrays or matrices.

(266) The product of two matrices is found by multiplying the corresponding entries and then adding the products.

(267) Inverse matrices are used in various mathematical applications, such as solving systems of linear equations.

(268) Hotelling's trace test is commonly used in multivariate analysis to test the equality of covariance matrices.

(269) The mathematician's groundbreaking work on diagonalizing matrices revolutionized the field of linear algebra.

(270) The study of combinatorics involves analyzing the properties of combinatorial matrices and their applications.

(271) The concepts of abstract algebra can be applied to analyze the properties of matrices and linear transformations.

(272) The inverse matrix of a product of matrices is the product of their individual inverse matrices in reverse order.

(273) The scientist develops new analytical methods to keep up with phosphate detection in complex environmental matrices.

(274) When working with matrices, arithmetic operations such as addition, subtraction, and multiplication can be performed.

(275) Monomorphism is a property that can be observed in many different mathematical objects, such as matrices and tensors.

(276) Circulant matrices have applications in the design of efficient algorithms for solving partial differential equations.

(277) The inverse matrix of a product of matrices is equal to the product of their individual inverse matrices in reverse order.

(278) Eigenvectors are a powerful tool in linear algebra that allows us to understand and manipulate the properties of matrices.

(279) Spectral normalization can be seen as a form of weight normalization that operates on the spectral norm of weight matrices.

(280) Alicyclic compounds, when incorporated into polymer matrices, can enhance the material's resistance to chemical degradation.



How To Use "Matrices" With Example Sentences.

(281) Alicyclics, when incorporated into polymer matrices, can improve the material's resistance to UV degradation and weathering.

(282) The selection of appropriate extractants is crucial for the successful extraction of target compounds from complex matrices.

(283) The transpose of a matrix with all elements equal to the sum of two matrices is equal to the sum of the transposes of those matrices.

(284) Hotelling's trace test is commonly used in multivariate analysis to assess the significance of differences between covariance matrices.

(285) Gelation is a technique that can be used to create matrices for drug delivery, and it allows for the sustained release of drugs over time.

(286) The concept of being prime to is not limited to numbers; it can also be applied to other mathematical objects such as polynomials or matrices.

(287) The transpose of a matrix with all elements equal to the difference of two matrices is equal to the difference of the transposes of those matrices.

(288) Isomorphism is a powerful tool for understanding the relationships between different mathematical structures, such as graphs, matrices, and functions.

(289) The transpose of a matrix with all elements equal to the product of two matrices is equal to the product of the transposes of those matrices in reverse order.

(290) The concept of a linear transformation is essential to understanding the behavior of matrices, which are used in a wide range of applications, from computer graphics to cryptography.

(291) The multiplicative property of matrices states that the product of two matrices is defined only if the number of columns in the first matrix is equal to the number of rows in the second matrix.



Learning English Faster Through Complete Sentences With "Matrices"

Sentences are everywhere.
Without sentences, language doesn’t really work.

When you first started learning English, you may have memorized words such as English meaning of the word "Matrices"; But now that you have a better understanding of the language, there’s a better way for you to learn meaning of "Matrices" through sentence examples.

True, there are still words that you don’t know. But if you learn whole sentences with "Matrices", instead of the word "Matrices" by itself, you can learn a lot faster!



Focus Your English Learning On Sentences With "Matrices".

Why Is Focusing on Sentences Important?
Sentences are more than just strings of words. They’re thoughts, ideas and stories. Just like letters build words, words build sentences. Sentences build language, and give it personality.

Again, without sentences, there’s no real communication. If you were only reading words right now, you wouldn’t be able to understand what I’m saying to you at all.

- The Word "Matrices" in Example Sentences.
- "Matrices" in a sentence.
- How to use "Matrices" in a sentence.
- 10 examples of sentences "Matrices".
- 20 examples of simple sentences "Matrices".

All the parts of speech in English are used to make sentences. All sentences include two parts: the subject and the verb (this is also known as the predicate). The subject is the person or thing that does something or that is described in the sentence. The verb is the action the person or thing takes or the description of the person or thing. If a sentence doesn’t have a subject and a verb, it is not a complete sentence (e.g., In the sentence “Went to bed,” we don’t know who went to bed).



Four Types Of Sentence Structure.

Simple Sentences With "Matrices"

A simple sentence with "Matrices"contains a subject and a verb, and it may also have an object and modifiers. However, it contains only one independent clause.

Compound Sentences With "Matrices"

A compound sentence with "Matrices" contains at least two independent clauses. These two independent clauses can be combined with a comma and a coordinating conjunction or with a semicolon.

Complex Sentences With "Matrices"

A complex sentence with "Matrices" contains at least one independent clause and at least one dependent clause. Dependent clauses can refer to the subject (who, which) the sequence/time (since, while), or the causal elements (because, if) of the independent clause.

Compound-Complex Sentences With "Matrices"

Sentence types can also be combined. A compound-complex sentence with "Matrices" contains at least two independent clauses and at least one dependent clause.



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