EXAMPLE Question 7.1.23 4-7-7 Let A= -7 4-7 and v= -7-7 4 Verify that 11 is an eigenvalue of A and v is an eigenvector. Then orthogonally diagonalize A. The number 11 is an eigenvalue of A with eigenvector (Type an exact answer, using radicals as needed.) 7.1.23 3-9 -9 Let A = -9 -9-9 39 and v= 3 Verify that 12 is an eigenvalue of A and v is an eigenvector. Then orthogonally diagonalize A. The number 12 is an eigenvalue of A with eigenvector (Type an exact answer, using radicals as needed.) 1 The vector v = 1 is an eigenvector of A with eigenvalue - 15. (Type an exact answer, using radicals as needed.) Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. Enter the matrices P and D below. √√3 7575 - -6 -6 -6 √√√6 -15 0 0 0 12 0 √6 0 0 12 2 √6 (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)