Find an invertible matrix P anda matrix C of the form such that A= has the form A = PCP-1. The eigenvalues of A are 3- i and 3+ i. The corresponding eigenvectors are v, = , respectively

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are 11 and 2. 6 4-2 4 6 -2 -2 -2 3 Enter the matrices P and D below. (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)

Find a 2 x 2 matrix A such that the entries of A are all real numbers and –4 is an eigenvalue of A, or explain why no such matrix exists.