Calculus eigenvalue

Question

For which value of k does the matrix A = [−2 k] [−4−7] have one real eigenvalue of algebraic multiplicity 2?

 

Answer 1

Solving for eigenvalue.

A-λI=0

(λ+2)(λ+7)+4k = 0

λ²+9λ+14+4k =0

λ=(-9 ± √(81-4(14+4k)))/2=2

when k=0, λ=2