(a) Let A, B, and C be two square matrices of the same dimension and A be an invertible matrix then (A-¹BCA) 2023 = A-¹B2023 2023 A. True False Justification: (b) Let A be an nx n matrix. The set of all nxn matrices X that satisfies (A²-31)X = O is not be closed under the matrix addition. True Justification: (c) If A and B are 6 x 6 matrices of rank 6, then AB also has rank 6. True False Justification: (d) If A is a 5 x 6 matrix of rank 3, then the solutions of Ax = 0 is has two parameters. True False Justification: (e) Matrix False Justification: in Z5 has two distinct eigenvalues. True False

Q: Compute the adjugate of the following matrix: 5 60 adj 4 -7 -5 -10 -4 -6 000 000 000

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Q: Find a basis for the row space of

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Q: Is the produ ct elementary. matri ces dalways OF two an swer. elementary ? Sustify your

A: The product of elementary matrices need not be an elementary matrix. Recall that any invertible…

Q: Use the matrix form of the Euclidean algorithm to find the greatest common divisor (165,312) for the…

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Q: Find matrix such that 5 3 -1] X+ 2 -3 1

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Q: to B=101 t00 select all true •If AB =Ithen BA=I AB=I 'AB=I but nut BA=I "BA-I inone of these %3D

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Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

A: We will find the required.

Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: Let A, B and C be invertible, nxn matrices with AB BA and I, the n x n identity matrix. If AXB-= I+…

A: Invertible Matrix: An invertible matrix is a matrix for which matrix inversion operation exists,…

Q: 3. Tell whether the statement is true or false. If true, provide a proof. If false, provide a…

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Q: (1) True or False? Justify your answer. (a) Let A, B, and C be two square matrices of the same…

A: for given three matrices with same dimension  and  is invertible,Again as matrix multiplication is…

Q: (18) Does a 2 × 2 diagonal matrix commute with every other 2 × 2 matrix?

A: We have to check

Q: Compute the adjugate of the following matrix: -7 3 -6 0 0 0 0 0 0 0 0 0 adj -7 0 -2 %3D | 2 -8 4

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Q: ( -10! BIf (21-A)-! evaluate the matrix A.

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Q: How do you know whether a matrix is invertible?

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Q: A diagonal matrix is a square matrix that if rotated to give the original matrix 1- right 2-Error

A: a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term…

Q: Suppose A is a square matrix. Show (a) A+A" is symmetric, (b) A – A" is skew-symmetric, (c) A= B+ C,…

A: Sum of symmetric and skew-symmetric matrix is matrix it self. Like for matrix A, Symmetric matrix =…

Q: Diagonalize the matrix 1 0 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix D…

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Q: Q5) Check whether the following matrix is diagonalizable or not. 7 -3 A = -9 -2 3 18 -8,

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Q: Express the matrix = [₁,1] - 9 and its inverse as a product of two elementary matrices. A =

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Q: 6. Let A be a 2x 2 matrix such that (a) The above equations can be written in the form A -1 0 -1 0 B…

A: The objective is to find the matrix B. heck whether the matrix B is diagonalizable or not and also…

Q: Is the matrix A invertible -1 2 3 -6 O True O False

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Q: Diagonalize the matrix [5 -14] 4 -10 A = by writing it as A = PDP-¹ P = D = P-1 =

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Q: -4 -4 -16] A = 16 -18 -56 -4 6 -51 That is, write A = LDU where L is a lower triangular matrix with…

A: We can make some row transformations to find the upper triangular matrix prime U', then from this,…

Q: X = 8 8 3 3 ; A = 2 42 0 1 -2 -3 7 3 3 2 9

A: Every matrix of order m×n is represented a linear transformation from Rn→Rm definition of T(x)=Ax

Q: Let A be a 2 X 3 matrix, B be a 3 X 2 matrix and v be a 3 X 1 vector. Indicate the dimensions of the…

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Q: Show that matrix multiplication is associative i.e. A(BC) = (AB)C when- ever the multiplication is…

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Q: Suppose A = *=([=3][=3][==] A6- -27 -15 50 28 = Find an invertible matrix P and a diagonal matrix D…

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Q: If we multiply a row in a matrix A by a real number r, JAl changes in r.

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Q: If A + 0 and B+ 0 are square matrices of the same order, then AB + 0.

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Q: 5. (16 points) Let A = [13¹], B = [-1¹ 63], and C = [29]. Compute each matrix sum or product if it…

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