Question

If A = [(1,0,0),(0,1,1),(0,-2,4)] and I = [(1,0,0)(0,1,0), (0, 0, 1)] and A^–1 1/6 (A² - cA + dI), then c and d are

(a)   –6, –11 

(b)    6, 11

(c)   –6, 11 

(d)   6, –11

Answer 1

Correct option  (b)  6, 11

Explanation:

The characteristic equation is |A – λI| = 0

λ³ – 6λ² + 11λ – 6  = 0

By Cayley’s Hamilton Theorem

⇒ A³ – 6A² + 11A – 6I = 0

⇒ A^–1A³ – 6A^–1A² + 11A^–1A = 6A ^–1I

⇒ A²– 6A + 11I = 6A^–1 

c = 6, d = 11