Answer to Question #115380 in Linear Algebra for Sourav mondal

Question

Let A be a 3 x 3 matrix A with eigenvalues
1, –2, 2. Find the trace of A + A². Give
reasons to justify your answer.

Answer 1

Eigen values of A are 1,-2,2 (Given).

Therefore eigen values of A² are 1, 4, 4.

So eigen values of (A+A²) are 2, 2, 6.

Trace of (A+A²)=Sum of eigen values of (A+A²)

= 2+2+6=10.

• Answer is 10.