DeterminantHard

Question

Given A = , I = . If A - λ I is a singular matrix then

Options

A.λ = φ
B.λ2 - 3λ - 4 = 0
C.λ2 + 3λ + 4 = 0
D.λ2 - 3λ - 6 = 0

Solution

|A - λI| = 0
⇒ = 0
⇒ = 0
⇒  2 - 2λ - λ + λ2 - 6
⇒  λ2 - 3λ - 4 = 0

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