Let A = [[1,3,5],[0,1,4],[-1,-1,2]] and vec(b) = [[2],[1],[0]].
(a) To solve the system Avec(x) = vec(b), Christina performed the following Elementary Row Operations in the order given and obtained the following augmented matrix:
[[1,0,0,-1],[0,1,0,1],[0,0,1,0]]
1. R3 -> R1 + R3
2. R3 -> -2R2 + R3
3. R3 -> -R3
4. R2 -> -4R3 + R2
5. R1 -> -5R3 + R1
6. R1 -> -3R2 + R1
For each of Christina's EROs, give the corresponding elementary matrix. Enumerate your elementary matrices in the order Christina applied them. (i.e. E1 corresponds to the first ERO.)
(b) Let R = RREF(A). Write R as a product of A and the elementary matrices you found in part (a).
(c) Use your product of elementary matrices in part (b) and an identity matrix to determine the inverse A^(-1).
(d) Solve the system Avec(x) = vec(b) using the inverse A^(-1) you found in part (c).