Question

8. Let A and B be two 3x3 matrices such that 3A = A^2 + AB and detA != 0.
a) determine the expression for B in terms of A
b) show that if A is an eigen value of B with corresponding eigenvector u then mu = 3 - () is an eigen value of A with corresponding eigen vector u
c) let B = [2,0,-1;0,2,-1;-1,0,1] find A

8.let Aand B t33 matries snch 3A-AtA and detA70 3 Ca) Determine the expresion thr B intn of t show that fAis an egen value f 3 espone egen nactor thn 5 3-A an eigen value f A ith carespondling digen vetor 2 2 L Let B Find -1 I E

Answer 1

) Given be tuo |3 x3 ma tvius, Such terat 3 A A AB and A A O a) To detemine exprenon tov B tlue teims A 3A A +AB A B A- 3A 2 A A 3 AA 2 B c) Let O B A - 3 I A = B+ 31 2 o- O 2 3 0 C 3 O CS Scanned with CamScanner