8 (10 points) 0 -1 -1 (a) (5 points) Determine whether the linear system 2 4 0 y -2 has: 1 -1 one solution, infinitely many solutions or nb solution. (b) (5 points) Prove that if A and B are invertible n x n matrices, then their product AB is invertible and (AB)-1 =B-1 A-1 9 [8 points) Let C= [ 1 2 4 0 -1 -2 -1 -2 -3 and b= — 0 (i) (6 points) Find the inverse of C. (ii) (2 points) Use part (i) to solve Cx=b. 10 (12 points) Diagonalize the matrix A = 1 0 0 0 1 1 0 1 1 if possible. 3
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