2. Compute (3C – 4D)², where C and D are arbitrary n x n matrices. Hint: Remember that matrix multiplication is not commutative, in general.

a: Diagonalize the following matrix, if possible [4 1 31 3 87 12 7 5

kindly answer it (1.2.20)

B = 2 [31] Write B and B-¹ as products of elementary matrices. • You must write out all of the matrices, and indicate what order you must multiply them to get B (and B-¹

Select ALL matrix multiplications that are valid given the following matrices: A = 23 2 B-0-|--A C = D= 4 5 6, E = 4 1 2 3 2 B*B D*D A*D E*BT B*D C*C C*CT A*B E*B D*B 1 = 456 1 2 3 789

Q2. Find the inverse of each of the following matrices a) A = [3³] [1 4 11 b) A = 2 8 3 12 7 4

2 3 A = 5 4 9 2 [1 0 2 3 1 3 Without multiplying the matrices, explain why A is not invertible.

2- Find the inverse matrix : 2 3 3. 1. 1 2 3 B = 2 5 3 3 -3 C = 2 -1 -2 -3 108 0 -4 -3

pls answer within 30 minutes

7. Derive and verify a Cayley-Hamilton formula for the inverse of an invertible 5 × 5 matrix.