Consider the matrix A

1 1 5 2. (REQUIRED) Consider the matrix A = 1 5 The matrix has eigenvalues of -4, 4, and 7. The 5 corresponding eigenvectors are X()=-4) = 0 ,X(X=() = -2 and x()=7) = (a) (2 points) Use this information to orthogonally diagonalize A. Arrange your eigenvalues in order from greatest to least in magnitude. Since 4 and -4 are tied, go ahead and use 4 first. (b) (6 points) Compute the spectral decomposition of A. That is, find three rank-1 matrices that sum up to A