lo o 1l l-1 2 a) Consider the following matrices: [1 0 01 [o 0 01 2 ,D = |0 0 Lo 1 1 2 -1 A =| 2 0 0 ,B = |0 0 0,C = I-1 2 1] 1 0 o]

Q: - ; Let A be a square matrix such that A? – 7A+ 81 = 0 (where I and 0 are the identity and zero…

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Q: Let A be the 2 x 3 matrix with entries aij = (i – 1)(j+1). %3D Which of the following is the matrix…

A: Let A=[aij] be a matrix of order 2×3This order means row =2and column=3A=a11a12a13a21a22a23According…

Q: a) Consider the following matrices: 1 0 01 A =| 2 [1 0 01 0 0,B = |o 0 o,C Lo o 1. [o 0 01 2 ,D = |0…

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Q: Find an example that meets the given specifications. 3 x 3 matrices A and B such that AB ± BA 0 0 0…

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Q: If A, B are 2 × 2 matrices such that AB = 0 then BA = 0. true false

A: As per our guide lines we are supposed to answer only one question. Kindly repost other question as…

Q: Let A and B be 2x2 matrices such that B is invertible. If det(A)=6 and det(B)=2, then det(A'B Select…

A: If A and B are two matrices, then, det(AB) = det(A).det(B) According to this property : det(A2 ) =…

Q: The identity Matrix is defined by 1 а. 1 1 1. b. 0 1 1 C. 1 1 d. 1 1 Select one: а. с b. d С. а

A: Here we identify the identity matrix.

Q: §3.7, Exercise 4. Let A, B,C be general n x n matrices. Simplify the expres- sion…

A: The given expression is A-1BA-1-1CB-1-1. Note that, if P, Q are invertible matrices, then we have…

Q: H.W 1-: The matrices A to K are -1.3 7.4 3 A =D -4 -1 5 B = -1 D = 7. 2.5 -3.9 4 -7 6. 3 6. 3.1 2.4…

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Q: Suppose A, B and X are matrices such that AX A = B, where 0 1 0 1 -2 1 3. -134 -5 1 2 , then X = |…

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Q: - 21 Prove that AB = kl, 1 4 Given that matrix A = 1 0 2 and B = 2 3 7 3 - 5 1 %3D - 3 1 1 where I…

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Q: 1. Consider the matrices: 1 [2 1 3 A = - 1 B = C 1 - 1 %3D 4 0 - 1 1 6. Compute the following: (a)…

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Q: |2 1. (exercise 3.1.18) Let A = 6 3 Find 2 x 2 matrices B and C such %3D that AB = AC but B # C.

A: Given matrix A=2163

Q: a) Consider the following matrices: [1 0 01 0 0 ,B = |0 0 0,C Lo o 1 1 0 0] 1 2 -1] A =| 2 -1 2 1] 2…

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Q: 1 0 0 0 1 0 9. Suppose M Which matrix is M1? %3D 0 3 1 1 00 1 3 0 0 1 0. -3 0. 0. 1 O (1 0 0 0 1 0.…

A: Finding inverse of M

Q: 23.37 For each of the following symmetric matrices, find an orthogonal matrix which diagonalizes it:…

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Q: 2. Let a = 2 and b = Calculate the following matrices. *a. aa c. b'b e. abT *f. a'b *b. ala d. bbT

A: As per guidelines only three sub-parts can be solved in one answer. For further solutions please…

Q: 3. Show that A and B are not similar matrices. [1 A = 0 2 1 -1 Lo 14.8= [2 1 1] 1 0 L2 0 1 ,B= 0

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Q: Consider the three following matrices: (1 0 10 0 0 -i 0 A=0 -1 0, B=| 0 0 0 and C =| i -i 1 0 0 -1 0…

A: Given A = 1000-10001B = 10000000-1C = 0-i0i0-i0i0 Then AB = 1000-1000110000000-1  = 10000000-1ABC =…

Q: Consider the three following matrices: (1 0 0 1 0 0 -i A =| 0 -1 0 B =| 0 0 and C =| i -i 0 0 1 0 0…

A: Trace- Let A be a matrix, then trace of the matrix A is the sum of the diagonal entries of the…

Q: 3. Show that A and B are not similar matrices. [1 2 0 A = 0 1 -1.B [2 1 11 ,B= 0 1 0

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Which of the following matrices is NOT symmetric? 1 0 0 0 0 1 0 1 O[ 5 6 7 6 3 2 7 2 1 7 -1 7 3 -1 0…

A: Consider the matrix 010000101 in the first option. For a matrix A to be symmetric, its transpose…

Q: Suppose A, B and X are matrices such that AX - A = B where 0 1 0 1 -2 13 4 -5 1 2 A D 3 B = 1 20 ,…

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Q: 1) Classify the following matrices into singular and non-singular matrices 2 4 3 a) 3 b)|-2 -4 -3 -2…

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Q: (b).Use the matrices а A d and 5 3 В 4 7 to illustrate Det AB Det BA det A. det B.

A: The matrix AB and  BA are:…

Q: H.W 1-: The matrices A to K are 3 -1 [-1.3 D = 2] 7.4 A B = !! -1 6 2.5 -3.9 -4 7 T 3.1 2.4 6.4 -7…

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Q: 1 3. В- (8 -3), С- 1 -2 -2 D= 1.1 Consider the following matrices: A= find: 1.1.1 Ax B 1.1.2 C 2D…

A: Note: As per company policy we have to solve only 3 subparts of the question. Please post the next…

Q: 1. Prove the following for any two matrices A and B of order ( 2 × 2 ). (A + B)² = A² + AB + BA + B2…

A: Here (a) and (b) are unrelated problems. These 2 are unrelated problems as anyone can be solve…

Q: [3 1 1 4 4 2 7 5 47 2 8 6. A1= 8 and let Ej and Eg be the elementary matrices [1 0 0 01 [1 0 0 07 0…

A: A-1=316414-2842287542 The elementary matrix are as follows, E1=1000010000100031 and…

Q: 3. The following matrices are elementary matrices except (a) 1 0 1 0 (b) 5 1 (3 (c) 1 (d) -3 -

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Q: Consider the matrices 3 0] -1 2 1 1 [1 4 2] A= B= C= 3 1 5 15 2] -1 0 1 3 2 4 6 1 3] D= E = -1 1 2 4…

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Q: 3 1] Write X = as a product X =E,EE3 of elementary matrices. %3D 50 E = E2 = ,Es= 00 %3D

A: The given matrix is: X=3150

Q: 7. Suppose that A & B are n x n matrices and AB B then: A. A I B. A Iif B nonsingular C. B AB D. B =…

A: If A and B are two n×n matrices such that  AB=B , this means that A=I(identity matrix) Otherwise it…

Q: Let A and B be n xn matrices. If AB = [0], then BA = [0]. (A) True B False

A: Matrix multiplication, is not communicative under multiplication.

Q: [1 0 1 10 1 1 1 0 ve B =|0 1 -1 Since the matrices are rowwise equivalent and EA = B, which is the…

A: Solution of the problem as follows

Q: -3] Let A be a 4 x 4 diagonalizable matrix, P = |–1 1 1 0 2 1 [1 01 P-1 D = |0 Lo 2 1 3 If P-1 A P =…

A: Given A be a 4×4 diagonalizable matrix. And given matrix is P=00−3−110102, D=100020002 and…

Q: 2. Consider the matrices [2 0 -1 D = |1 4 5 4 [2 -1 0 1 1 0 3 A B 3 and F = 0 15 2 (a) Show that A,…

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Q: Given that matrices A and B O 2] A = |1 0 2 lo o 1] [o o 21 [o 2 and B = 0 Lo 1 01 Where 1 2 3. Find…

A: A=002102001 and B=020012013

Q: [1 0 1 Consider the matrices A = 0 0 0 [1 2 30T B =0 1 20 %3D Lo 1 1 0 1. [1 C =0 0 01 1 0 0 4] And

A: conditions of a echeleon form- 1)-leading element in a row should be 1. 2)-number of zeroes before…

Q: [4 1 21 tA-3 4 2. B-1 -2 3, and C-5 0 2 Lo 3 2] [-1 0 5 [1 2 -3] [1 4 -3) 1 -1 1 [s 20 Find the…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Let A, B and C be the matrices A= 0 -7 8 0 0 2 Calculate |ABC). 20 -1 -24 √20 0 Vào 00 CH c-{" 0 1…

A: Given, A=15-10-78002,B=-200-120-2401'C=100001103010

Q: Consider the following matrices. 1 A = 1 B = -2 -2 10 -12 8 Find an elementary matrix E such that EA…

A: Topic:- matrix algebra

Q: Show that AB and BA are not equal for the given matrices. 1 1 4 B = 1 1 4 4 A = 1 1 4 5 1 1 4 4

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Q: (a) (MP) Verify that det(AB) = (det A)(det B) for the following matrices: 1 -2 3 1 0 2 A = -2 3 1 B…

A: given matrix  how to find determinant

Q: Let A = 2 O 5 31 O-36 5 Find unitary matrix U and a diagonal matix D Such that U₁AU = D.

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Q: One of the following matrices is not invertible 4 2 9 1 0 03 7 4 1 a) 0 0 54 b) 5 6 0 0 0 6 2777 40…

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Q: 30. Which of the following matrices is not diagonalizable? [3 2 5 (a) 0 4 7 0 0 9 [1 2 0 (c) 0 1 0 0…

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Q: If A, B are 2 × 2 matrices such that AB = 0 then BA= 0. | O true O false

A: Please refer to the image below.

Q: 1 4 [5 0 lo 4 -3] b) Given D = -2 3 1 -2 1 85 72 -54] A =| 50 32 -24. -35 -24 18 Find a matrix BT ,…

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