2.11. Orthogonally diagonalize the matrix A cos a sin a sin a -cosa Hints: You will get real eigenvalues in this case. Also, the trigonometric

Orthogonally diagonalize the matrix

Hints: You will get real eigenvalues in this case. Also, the trigonometric identities sin 2x = 2 

sin x cos x, sin2 x = (1-cos 2x)/2, cos2 x = (1 + cos 2x)/2 (applied to x = α/2) will help to 

simplify expressions for eigenvectors.

2.11. Orthogonally diagonalize the matrixAcos asin asin a-cosaHints: You will get real eigenvalues in this case. Also, the trigonometric identitiessin 2x = 2sin scos s, sin? > = (1 - cos 2r)/2, cos? = = (1 + cos 2x)/2 (applied tox =a/2) will help to simplify expressions for eigenvectors.