1. Given the matrix A = [ ]] a) Find eigenvalues and eigenvectors for A. b) Is the matrix A diagonalizable? Explain why or why not. 2. Given the matrix A = [_12 4] a) Find a matrix P such that -1AP is a diagonal matrix. b) Compute the product P-1AP to compute the diagonal matrix D = P-1AP that is similar to matrix A. 3. Complete each of the following: a) Define "Symmetric matrix" b) Define "diagonal matrix" c) Define "orthogonal matrix" d) Describe some of the favorable properties of a diagonal matrix. 4. Given the matrix A = 0 -2 o a) Find a matrix P that will orthogonally diagonalize the symmetric matrix A. b) Write the product P-1AP