Answer to Question #208985 in Linear Algebra for Anusha

Question

Evaluate 𝒂 so that the sum of the eigen values of 𝑨 is 10. [ 𝑎 4 −2 1 3 0 −6 4 𝑎 ]

Answer 1

Given matrix A = a 4 -2

1 3 0

-6 4 a

For finding Eigen values,

Consider characteristic equation,

|A-tI| = 0

t³ - t²(3+2a) - t(16-6a) - (3a²-4a-44) = 0

We know sum of the roots is -(-(3+2a))/1

= 3+2a

Given sum of Eigen values is 10

So, 3+2a = 10

2a = 7

a = 3.5 or 7/2