1 a. Verify that A? = I when A 101 -8 b. Use partitioned matrices to show that M² = I when 0 0 0 0 2 1 |-8 -1 1 M [10] -1 0 3 1 8 II

Q: Let -1 7 -1 A = 1 15 -2 (5a) Find a 3 × 3 matrix P and a diagonal matrix D : 13 such that A = PDP-…

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

A: Do as given in the question than verify it is true or false.

Q: 3. Let A = 1. ). Compute eat in two different ways: (a) by exponentiating the equivalent diagonal…

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Q: 3: For the matrices, A = [1 and B = 01 -31 (a). Show that, (A+ B)" AT +B". (b), Show that, (AB)-1 =…

A: Show that  a) (A+B)T= AT +BT  b) (AB)-1= B-1A-1  For the matrix A and B .

Q: Which of the following matrices corresponds to the elementary row operation 3R1 + R2 → R2 on.a 3 x 3…

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Q: Suppose matrices M and N are the proper sizes so both products MN and NM are defined. Is the…

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Q: If A = (3), B = -10 33(, ) and C= (G° - 13) determine the matrix X such that AXB = 71, where I is…

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Q: 2. Compute (3C – 4D)², where C and D are arbitrary n x n matrices. Hint: Remember that matrix…

A: To compute, 3C-4D2

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: -1 -[::] Determine the dimensions of Nul A and Col A for the matrices. A = 4 7.

A: Before finding the column space or null space, we will reduce the given matrix to its reduced…

Q: Which of the following matrices are diagonalizable? Justify your claim. 5 -18 -32 a. M, = 0 5 4 2 -5…

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Q: Let 1 -2 4 A = 0 -1 0 [1 2 P = 0 1 -1 and 0 0 -1 0 0 1 Given that P diagonalizes A, then compute…

A: Definition: Suppose A is a diagonalizable matrix, then there exists an invertible matrix P such…

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: 3. Compute the indicated matrices if: [1 A = |0 -1 17 2 B= c=| 9 D=; : [1 2 -1 li 0 [1 3 14 2 a) ЗА…

A: From the relations of matrices;   A-BT=AT-BTATT=A   Given; A=120-170…

Q: 7 Show that A = 13 and B = 4 2 are similar matrices by finding an invertible matrix P satisfying 2 A…

A: Given,A=7-132-4 abd B=1-2-22Let,P=abcd , and P=ad-bc=nSo, P-1=1nd-b-ca where n=ad-bc=dn-bn-cnan

Q: Which of the following matrices are in RREF? (: ) (1 10 7 0 1 9 0 0 1 1 14 1 1 - 1 0 0 5 1 1 10

A: Solution

Q: Given the matrix B= then the characteristic polynomial is: 31 O 1? +5A - 3 O A2 -5A - 3 O 12 +5A +3…

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Q: 13. Find matrices A so that a. A +0, but A² = 0 b. A? + 0, but A³ = O Can you make a conjecture…

A: First we will find matrix which for each case a. and b. then we will try to make a conjecture on the…

Q: Let A, B, and C be invertible matrices. Then (4C2BTA-1)-1 is equal to 글A(BT)-1C-2 None of the…

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Q: Which of the following matrices corresponds to the inverse of the elementary row operation. 3R1 + R2…

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Q: Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below. 7…

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Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix x + y = 1   x-y=2

A: x+y=1 x-y=2 We need to find the inverse using A-1 =(1/detA)adj A

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: Suppose T:R2 -> R² is defined by multiplication by 4 A = [17 -4. What matrix defines T1 by…

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Q: Let A, B, and C be invertible matrices. Then (4BT A-1C²)-1 is equal to None of the mentioned equal…

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Q: 1. Find a matrix K such that AKB = C, given that: 1 4 8 -61 -1 6. [2 0 ; B = 6 -2] A = -2 3 ; C: 6 1…

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Q: Which of the following 3 x 3 matrices are in row-echelon form? Note: Mark all of your choices. 0 1 0…

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Q: Consider the following matrices: 1. 2 3 [1 -1 A = 4 5 6. and B = 2 1 7 8 9. 3 -2 Compute the…

A: We can solve this problem using product of two matrix.

Q: Use the following matrix to compute 6A. 0 6 - 1 A = 4 1 B= 11 -5 2 -2 6A = O

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Q: 4. Express the following matrix A and its inverse (A-1) as products of elementary matrices, 1\ A =…

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Q: 1. Compute the condition numbers of the following matrices relative to || I. [] [ 3.9 1.6 b. a. 6.8…

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Q: Given the matrices below and that A = LU, complete L¬1,U-1, and A-1. 1 -2 -1 1 01 -2 -1° A= 2 -3 -5…

A: We use Gauss elimination method to find L-1, and U-1. After that by using (LU)-1=U-1L-1, we find…

Q: [1 Find a matrix A = -4 -51 = l3. y] 1 z such that A² 10 %3D Lo 1. Lo

A: Given A=1xy01z001 A2-0-4-50010000=I3 To find Matrix A:

Q: 13. Suppose that a 3 × 3 matrix A factors into a product 1 0 1 Determine the value of det(A).

A: It is known that for n×n matrices A and B detAB=detAdetB                      (i) Given…

Q: Compute the multiplicative inverse of the following matrix (If exist) 3 A 12 E 12 4. 4. B 12 F 12 3…

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Q: If A₁ = [a, b₁ [d₁ e₁ fi 3 real numbers, show that: 9. (A₁ + A₂) + A3 = A₁ + (A₂ + A3) 10. (k+h) A₁…

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Q: 1. Consider the following 3 x 3 matrices, [4 1 31 2 1 41 A = 0 -2 1 B = -1 3 13 3 2 5. (a) Calculate…

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Q: Consider the matrices 0 10 A = t -2 8 -6 B = 3 k -11 -2 8k C = 4 9 -7t with t,kER. The result of…

A: topic - matrices

Q: If A, B, and C are 5 x 5,5 x 3, and 3 x 9 matrices respectively, determine which of the following…

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Q: Which of the following matrices corresponds to the inverse of the elementary row operatio 3R1 + R2 →…

A: We have to find true option

Q: (a) Let A be an m × n matrix, and let B be the result of performing a single elementary row…

A: We have to prove that following Statement.

Q: consider the following matrices with given dimensions А: 3 х 4 B: 3 x 4 C: 4 x 2 D: 4 x 2 E: 4 x 3…

A: If a scalar quantity is multiplied with matrix then dimensions of new matrix remain same.

Q: Consider matrices A and B of size 3x3. If it is known that A =-2 and |B|=6, then the result of -3B°…

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Q: 1. Use the following matrices to compute the indicated expression if it is defined. 3 5 21 1 D =|-1…

A: The matrix product can be calculated by multiplying the row of the first matrix by the column of the…

Q: 4. (a) Show that the following matrix is diagonalizable. (b) Find a matrix P that diagonalizes A.…

A: A matrix is said to be diagonalizable if the algebraic multiplicity of the eigen value is same as…

Q: 1. Consider the matrices: 4 A = 1 B = 2 Compute the following: (a) (AB)-1 + BA, (b) BC – IBC

A: Given: A=40-12, B=1012, C=1-112

Q: 2. Consider the following matrices : 1 2 -1 3 1 and B = 3 2 A = 4 2 -1 -2 5 (a) Find At. (b) Use the…

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