Could someone please let me know how I would go about accomplishing the following tasks. Thank you.
Let A = [[4,0,0],[0,1,3],[0,3,1]
a) Find the Eigenvalues of A.
(lambda - 4)(lambda - 4)(lambda + 2)
So the eigenvalues are 4, 4, and -2.
b) For each eigenvalue, find a basis for the corresponding eigenspace.
c) Use these bases vectors to construct an orthogonal matrix P.
d) Verify that is a diagonal matrix.