For λ ∈ R, let f(λ)=det(A-λ I) where A=[1 2 -1 3] and I is an identity matrix of order 2 . The minimum value of f(λ) is equal to

Question

For λ ∈ R, let f(λ)=det(A-λ I) where A=[1 2 -1 3] and I is an identity matrix of order 2 . The minimum value of f(λ) is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We have f(λ)=det(A-λ I)=[1-λ 2 -1 3-λ] =(1-λ)(3-λ)+2 =λ2-4 λ+5=(λ-2)2+1 Clearly, f min (λ=2)=1

Q. For $λ \in R,$ let $f (λ) = d e t (A - λ I)$ where $A = [1 - 1 23]$ and $I$ is an identity matrix of order $2$ . The minimum value of $f (λ)$ is equal to