If A = 1 - 3 2 k and A 2 - 4 A + 10 I = A , then k is equal to

Question

If A = 1 - 3 2 k and A 2 - 4 A + 10 I = A , then k is equal to, 0, - 4, 4, 1 or 4

MARKS App · Accepted Answer

A 2 - 4 A + 10 I = A ⇒ 1 - 3 2 k 1 - 3 2 k - 4 1 - 3 2 k + 10 1 0 0 1 = 1 - 3 2 k ⇒ − 5 − 3 − 3 k 2 + 2 k − 6 + k 2 − 4 − 12 8 4 k + 10 0 0 10 = 1 − 3 2 k ⇒ 1 9 - 3 k - 6 + 2 k 4 + k 2 - 4 k = 1 - 3 2 k ⇒ 9 - 3 k = - 3 , - 6 + 2 k = 2 ...(i) and 4 + k 2 - 4 k = k ⇒ k 2 − 5 k + 4 = 0 ⇒ k = 4 , 1 But, k = 1 does not satisfy the Eq (i).

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