12. Consider the matrices O 1 0 [o 1 A B = 1 0 1 1 0 1 0 1 0 0 07 O 10 0 0 0 0 1 0 1 0 0 1 [o 0 0 1 0] 1 0 1 1 0 1 0 C = D = 0 1 0 1 1 _0 0 1 0 а. Use row (and/or column) operations to find the determinants of these matrices. b. Write the 6 × 6 and 7 x 7 matrices that follow in this pattern and state their determinants based on what you have seen.

Q: If A,B are symmetric matrices, then prove that (B A-1)T (A-1BT)-1 = I.

A: Given that, A,B are symmetric matrices.

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

A:

Q: Let T,(x1,x2) = (+4x1 – 5z2, +1æ1 – lz2), and T2(x1,X2) = (- 321 – 5æ2 , +5æı + 8x2). Write the…

A: To find the standard matrices for T1,T2 and T10T2.

Q: Find the classical adjoint of the following matrices. -4 0 0 (b) (a) (A11 A12 A21 A22) (d) /3 6 7…

A: Hey since there are multiple subparts the first three is answered. If any particular subpart has to…

Q: Find 2 × 2 matrices A and B such that т 6 ]A+[, -1 JA+I 5 -5 ]B = [ 4 -6. ] and -2 -1 4 0 -2 -4 3 -4…

A: Given: The equations  06-1-1A+5-534B=4-60-2T0-211A+-4-8-3-6B=3-47-3T

Q: 3- -4 0 1 2 1 - Find the adjoint matrix adj(A). 0 -1 Let A = 3 1 -2 3 -1 -1 2 a) 1 b) -1 2 1 2 -1 0…

A:

Q: 5. Compute the determinant of 27 10 -27 35 3 -8 11 A = 14 -14 -5 -18 - -3 4 Does the inverse matrix…

A:

Q: 2. Let (r x s) denote an r x s matrix. Find the size of those matrix products that are defined. а)…

A:

Q: Prove that if A and B are two similar n x n matrices, then they have the same determinant and the…

A: (.) Similar matrices: Two  matrices  are  similar if there exists a   non - singular matrix such…

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

A:

Q: -() --()-() 3 6 3 3 1 2 1 2 1 1 2 1 3 1 2 3 2 2 A = 3 1 2 В C = 4 4 3 4 4 3

A: Claim: We have to find E such that EA=Bi.e. E=BA-1 And F such that, FA=C i.e. F=CA-1 A=121312443then…

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: 1 6. Given that A = -1 and B = Which of these matrices equal (AB)'? -2 0 (c) 0. (a) 0. (b) (d) -2 -2…

A:

Q: -3 4 B = -1 | %3D 4 | 0 4 3. C = -2 5 1 D = 4 -2 0 1 Using the above matrices find DB

A: Given matrices are

Q: 7 A = 0 2 -5 l-9 3 -8 39. Determine the determinant of the matrix A. a. 106 b. 530 c. 265 d. 670 40.…

A:

Q: Let A be a 2 x 2 matrix a If ad – bc + 0, then A-1 ad-be ad-be ad-e ad-be. such that [1 AA-1 = A-'A…

A:

Q: 1. If A and B are real square matrices, show that a) b) c) (A+AT) is symmetric, (A -AT) is…

A:

Q: Let A and B be the matrices as shown. '1 2 1 1 2 1 ^ - ( ²³ ) ·- - 6 ÷ ³) A = 0 5 1 B = 2 -1 4 2 −1…

A:

Q: Let A and B be unitarily equivalent complex matrices. Show that A is normal if and only if B is…

A:

Q: Explain why det (BPB¯¹) = det(P) for any matrices P and B. Assume both sides of the equation are…

A:

Q: -1 Suppose A, B, C, X are invertible n x n matrices. Solve the matrix equation C(B1X) = (B-²C-1) B²…

A: If A and B are nxn invertiable matrices then(AB)-1=B-1A-1

Q: If a 4 x 4 matrix A with rows v1, v2, v3, and 4 has determinant det A = 3, 601 + 704 v2 then det √3…

A:

Q: Find a matrix C such that A = CB for the matrices 1 4 5] A = |-2 0 1 3 1 0 -4 0 2] B= | 1 4 5 5 5…

A:

Q: Consider the matrices 1 -1 2 -4 A = 2 1 and BA= 3 -7 -1 1 4 1 (a) to find A-'. Show that A is…

A:

Q: Corollary: if A is totally unimodular then the mat: -A ), A are also totally unimodular. ) -A

A: Introduction: If every square submatrix of matrix A has determinant 0, or ±1, a matrix A is entirely…