Question

Consider the matrices -2 -1 1 4 1 A = B = 4 -2 4 -2 -2 4 -2 1 -1 (a) Verify that they are diagonalizable and that they commute. (b) Find the eigenvalues and eigenvectors of A and verify that its spectrum is nondegenerate. (c) Show that the eigenvectors of A are eigenvectors of B as well.

Answer 1

Explanation to answers are shown in the attachment

Explanation:

This is a long solution but the detailed step by step and appropriate mathematical manipulation has been done as shown in the attachment.