Thread: Gauss-Jordan reduction inverse

Carry the Gauss-Jordan reduction of
0 4 2
1 2 0
2 0 -2

far enough to show that it has no inverse.

The steps I've done thus far are:
swap row 1 and 2
Row3-(2*row1)
(1/4)*row2

and i got as my matrix:
1 2 0|0 1 0
1 1 1/2|1/4 0 0
0 -4 2| 0 -2 1

Is that the furthest I can go? and what signifies exactly that there is no inverse?

Thanks in advance

I think you're in the wrong algebra section--this should go under linear algebra. But you should reduce it until you find two rows which have the same numbers. So for instance, divide the top row by two, the bottom row by two, then in the resulting matrix, take the last row and subtract it from the second row. You'll get that the first and second rows are the same, and therefore it's not invertible. This means that the matrix represents a linear transformation which cannot be uniquely reverse by matrix multiplication--i.e. there is no matrix such that it and this matrix, when multiplied, produce the identity matrix.