Question 2

(a)

(b)

Given matrix A:

(i)

(ii)

(iii)

TO

A = 1

O

-31

1

1

L2 0 5

Show with working that the eigenvalues of matrix A are 1, 2 and 3.

Compute the eigenvectors of the corresponding eigenvalues.

Hence obtain the eigendecomposition of A.

Prove that a 2x2 symmetric matrix B=

diagonalizable.

(6 marks)

(9 marks)

(8 marks)

with a, b, c ER is always

(7 marks)