5. Let A and B be the matrices A = B = (a) Calculate A" A, simplify as much as possible. (b) Calculate BB, simplify as much as possible. (c) Calculate (AB)"(AB). HINT: If you use parts (a) and (b), together with some of the rules for matrix multiplication, it is not necessary to calculate AB. 6. A real matrix A is called normal if AAT = ATA. (a) Why is a non-square matrix never normal? (b) Find all real values of r such that the matrix 4 - (2 1 ) is normal. 7. Let t be a positive real number, and let u, v and w be the vectors u = 2j, V2t 2Vt 2Vt w - H+ +1k. (a) Let 0 be the angle between u and v. Determine cos(0) as a function of t. (b) Find the angle between u and w. Give your answer as a (rational) multiple of 7 in radians. (c) Find a vector that is perpendicular to both u and w