I'm getting the same answers as the teacher when I re-do it by myself. But when I try to check it to make sure the answers fit into the original problem, it doesn't equal zero.

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She defiantly did question 2 wrong, Rag is right she did not reduce the determinant by 2.  Remember when you reduce the determinant you have to square it so you actually divide by 4 since 2 squared is so the determinant reduces to the square root of 57.