10. (i) What is the matrix A of a linear transformation from C4 to itself with respect to

the basis {V1, V2, V3, V4} of C4?

Find the matrix of the linear transformation from C4 to itself given by

x

0

Z

=

where V₁ =

x+iz

y - it

x - iz

y + it

(9).

0

, V₂ =

(9). (0-0)

1

(ii) Define the terms symmetric matrix, and orthogonal matrix (over R). Find the

600

eigenvalues and orthogonal eigenvectors of the matrix B =

052

and hence

022

find an orthogonal matrix P such that PT BP is diagonal.