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

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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: