4 3) Consider the matrices A 20 0 i) Evaluate each of the following or state why it is not possible: a) AB b) BA C) BT C d) C + B [4] ii) Find the determinants of A and C above. Show explicitly that |A/ = |A-1. Find |40"| [3] iii) Consider the matrix equation: W Solve your matrix equation by using either Gaussian elimination and back substitution or by finding and using the inverse matrix. (NB: you will get no marks for a solution using ad hoc methods of solving simultaneous equations.) [8] 11 0 -30 iv) Show that -2 is an eigenvector of ! -6 0 16 and find its 6 1 -15 eigenvalue. Find the other eigenvalues. [10]