Find one eigenvalue and its corresponding eigenvector of the symmetric matrix A by hand. Compute the other two using MATLAB. Using MATLAB, show that any two eigenvectors corresponding distinct...

Find one eigenvalue and its corresponding eigenvector of the symmetric matrix A by hand. Compute the other two using MATLAB. Using MATLAB, show that any two eigenvectors corresponding distinct eigenvalues are orthogonal, and diagonalize A with an orthogonal matrix.

Q10.

1. Find the eigenvalues of matrix A. Can you diagonalize it? Explain.

2. Find the eigenvalues of A. The matrix A has two equal eigenvalues, but it still has three linearly independent eigenvectors. Diagonalize A with an orthogonal matrix using MATLAB.

3. Find the

²
inner product of
 Also compute

².

4. Over the interval
 show that

_L
²
 for
 and that
_L
²

5. A permutation matrix is a matrix obtained by swapping one or more rows of the identity matrix. Prove that a permutation matrix is orthogonal.