4. (a) (6 points) Let A and B be any symmetric matrices of the same size. Show that A+kB' is symmetric for any scalar k. (b) (7 points) Let A be any real matrix and z be any real column vector. Show that z'A' Az 0. That is, the entry in this 1 by 1 matrix is non-negative. Hint: Write down the entries in Am. (c) (7 points) Let A be a matrix and c,d are non-zero scalars. Find all possible A satisfying cdA = A but ce #d-!. Hint: Use the definition of equal matrix