I just found the determinant of a matrix and it was 0. I know this means that the linear transformation from which the matrix was derived isn't isomorphic. Why is this, though?

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- May 8th 2007, 06:51 PMbuckaroobillGeneral question about determinants
I just found the determinant of a matrix and it was 0. I know this means that the linear transformation from which the matrix was derived isn't isomorphic. Why is this, though?

- May 8th 2007, 07:33 PMThePerfectHacker
That means the standard matrix, A, is not invertible. Which means what? Let

**b**be a coloum vector. The equation A**x**=**b**either has no solutions or infinitely many. In either case the solutions for**x**IS NOT unique. Thus, the map cannot be both one-to-one and onto.