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 Let -1] 3. 2

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

A:

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: Compute the adjugate of the following matrix: 5 60 adj 4 -7 -5 -10 -4 -6 000 000 000

A:

Q: Let - (; ;) 5 3 A = 2 1 a) Calculate A-1 by any method. b) Using your answer to part (a), explicitly…

A:

Q: Express the quadratic form (c₁r1 + c₂2+...+Cnn)² in the matrix notation TA, where A is symmetric.

A:

Q: aj bị c1 adjA if A = |a2 b2 c2| is a non-singular matrix prove that A: detA аз b3 C3

A: Matrix A is a non-singular matrix. This means; det A ≠ 0    A =a1b1c1a2b2c2a3b3c3adj A…

Q: 2 + jai a2 +j Suppose A = is a 5– jaz 3 – ja4 Hermitian matrix then a. aj any real number b. aj = 5…

A:

Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: Solve the matrix equation AX + C = AXB there 1 2 a) A = (-1 ½) · B - (-6 3 ) a = and C = 27 5-1 -22…

A:

Q: Demonstrate that A A-1 = A-1 A = I

A:

Q: Let 0 9. A = = [6 0 Is it possible to find a two by two real matrix B such that A = eB₂

A:

Q: 13.) Determine the matrix: s P 6-8 3 ។ -3 the dimension X 10

A:

Q: 3 4 Let X and Y in the set of 2 × 2 matrices, M22. %3D -11 2 3 Determine whether A = or B are in…

A: Given  X=2-121, Y=34-11 and A=0-1181, B=2312

Q: Prove that (A + B)² = -(A + B) in matrix..

A:

Q: Find a 2 x 2 matrix such that 3 -2 -2 = 61

A:

Q: Find all matrices B that commute with 1 + i (¹+1) :). 0 A = That is, for which AB = BA.

A: Let B=abcd be the matrix such tghat AB=BA

Q: Q5) Check whether the following matrix is diagonalizable or not. 7 -3 A = -9 -2 3 18 -8,

A:

Q: ebra to show that for n x n matrices A,B,C and n x 1 vector rtible and ABC then the matrix equation…

A:

Q: 1 -1 2 a) Find the matrix A if (3A) =0 2 0 3 -1 4

A:

Q: agonalize A and use the diagonal matrix to compute A100

A:

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

A:

Q: Find the power of A for the matrixA16

A:

Q: 1 8 Which of the entries in the matrix 2 -3 -7 9 A) 4 B) 1 Ⓒ-3 (D) -6 -61 4 has-37 as its cofactor?…

A: We have to find correct option by finding element whose cofactor is -37

Q: P-1 Show that A = 30 -23 42 -32 and B -2 -2 3 E = are similar matrices by finding an invertible…

A:

Q: 5 3 [B] -5 -6 i.e. write A = LU where L is a lower triangular matrix with 1's on the diagonal, and U…

A:

Q: Select all statements below which are true for all invertible n x n matrices A and B DA. AB is…

A:

Q: Find a P'LU factorization of the given matrix A. (Enter each matrix in the form [[row 1], [row…

A: