The possible values of scalar k such that the matrix A - 1 - kI is singular where A = 1 0 2 0 2 1 1 0 0 , are

Question

The possible values of scalar k such that the matrix A - 1 - kI is singular where A = 1 0 2 0 2 1 1 0 0 , are, − 1 2 , 2, − 1 , 1 2, 1 2 , − 1 2, − 1 , 1

MARKS App · Accepted Answer

A - 1 - kI = 0 A A - 1 - kI = 0 A ≠ 0 I - kA = 0 I k - A = 0 ⇒ A - 1 k . I = 0 ⇒ A - λ I = 0, where λ = 1 k ⇒ 1 - λ 0 2 0 2 - λ 1 1 0 - λ = 0 ⇒ 1 - λ - λ 2 - λ + 2 0 - 2 - λ = 0 ⇒ - λ 3 + 3 λ 2 - 2 λ - 4 + 2 λ = 0 ⇒ λ 3 − 3 λ 2 + 4 = 0 ⇒ λ = 2, 2, − 1 ⇒ k = − 1, 1 2

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