Question

14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For each matrix A below, follow the proof of Theorem 3.46 step by step to find inmrn ible matrices P and Q such thet

for (a) plz thank u!!?

Answer 1

The given information A = [1 2 0 2 4 1 1 2 2] Q = [1 0 0 - 2 1 0 3 - 2 1] Aq = A^- 1 = [1 2 0 0 0 1 0 0 0] A^- 1 = {(1,2,0),(0,0,1),(0,0,0,) } D_2 = [1 0 0 0 1 0 0 0 0] Let { x = (a_1,b_1,c_1) , y = (a_2,b_2,c_2) z = (a_3,b_3,c_3) } = B (A1,b1,c1 = 1 (1,2,0) + 0 (0,0,1) + 0 (0,0,0) implies (a1,b1,c1) = (1,2,0) (a2, b2,c2) = 0 (1,2,0) + 1 (0,0,1) + 0 (0,0,0) implies (a2,b2,c2) = (0,0,1) (a3,b3,c3) = 0(1,2,0) + 0 (0,0,1) + 0 (0,0,0) implies (a3,b3,c3) = (0,0,) implies = 1/2(1,2,0),(0,0,1),(0,0,) } is the eq^n is PAQ = D_2 implies PA^1 = d_2 implies P cacot be invertible