Find the elementary matrix E such that EB = A where 2 -12 2 1 1 A = 4 0. -2 and B = 24 %3D | 6. -8 3 6. -8 3

Q: 1. Let, A = -1 21 Find the matrix -5A3 + 2A? + 4A + 512. 9 21

A: Given: A=-1292 Determine A3. A3=-1292-1292-1292=192922-1292=-14218962

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

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Q: Let A =  -2 1     0 3     and    B =  2 -3     1 −2. Find a matrix X satisfying the matrix…

A: The given matrices, A=-2103 and B=2-31-2 We have to find the matrix X, that satisfies 2A+X=3B

Q: Diagonalize the given matrix A and hence find A². 10 -2 -5] 2 3 3 5 A = -2 -5

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Q: Solve the matrix equation AX = B for X. 1 3 11 B = 33 A= 5 4 X=

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Q: Solve the matrix equation AX = B for X 8 1 A = B = -1 2 - 13 X =

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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: 9. Do the columns of the matrix A = 7. span R

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Q: Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix…

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Q: Express the matrix A = as the product of elementary matrices. 1 2 2 10 2 31

A: Elementary square matrix :- A square matrix of order n is said to be an elementary square matrix if…

Q: Find the rank of the matrix 3. 5 9 -3 5 -11-5 -3.

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Q: Solve the matrix equation AX = B for X. A = 1 -2 -3 4 6 -1 -2 - 1 1 7 B= 6 5

A: Given: The matrix A=1-2-3-1461-1-2 and B=765. To find: Solve the matrix equation AX=B for X=???.…

Q: -5 4] -5 2 1 ||

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Q: Find A-5B. -7 9-4 6 - 6 B = 3 -4 -9 A= 3 -7 12 15 -10 A-5B% D 11 3. (Type an integer or decimal for…

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Q: 10. From the above, find the value of both the matrices A and B are the same.

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Q: (-1 7 -5 7. Let A = -4 11 -6). Diagonalize A if possible or explain why the matrix A is not -4 8 -3.…

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Q: 7. (S.15). Find the inverse A-1 of the matrix -2 -3 A = 0 2 -1 -1 -2 3

A: Matrix Question

Q: Which one of the following is an upper triangular matrix? .a 5 3 1 0 -5 2.6 0 0 5 .b

A: Upper triangular matrix is the matrix in which the values below the main diagonal are zero and the…

Q: Express the matrix A-¹ as a product of elementary matrices using In= EkEk-1...E₁A. 100 220 313 A =

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Q: Find 2A-l if we have the matrix 2 1

A: A=32102A=232102A=2×32×22×12×02A=6420

Q: 3. Let A=1 -1 4 -3 7 and B= 6 -24 -6 18 Find the matrix X that satisfies the matrix equation…

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Q: 3. Find the indicated matrix. 13 04 =[28] and B = [96] 26 -16 Let A et A = Find 3A + B.

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Q: Q10. If the adjoint matrix (ACT) of a matrix A is given by 2 2 of A is (-2 1 2), then the det (A)…

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Q: Find a non-zero 2 x 2 matrix such that -5-2 6 15 -[88]- =

A: We have to find a non zero matrix such that the given rfelation satisfies.

Q: Q1/ If 1 4 -3' -3 8Y 2 -3 -6,B = 1 1 and C = 2 11 -2 6. -3 are three matrices find |D"| where D = A?…

A: The given matrices are: A=1042-3-6902 ;       B=30-30111-26    and     C=0-38021-301

Q: Find the rank of the matrix for n = 2, 3, and 4. Can you find a pattern in these ranks?

A: Given, the matrix                  We have to find the rank for n = 2, 3, and 4. Also, find a…