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## Homework Statement

Find the inverse of the following using row reduction. If it does not exist, indicate clearly why.

3, 0, 6;

1, -2, x;

1, 2, 1;

**2. The attempt at a solution**

I started by augmenting with a 3 by 3 Identity matrix:

3, 0, 6, 1, 0, 0;

1, -2, x, 0, 1, 0;

1, 2, 1, 0, 0, 1;

Then I started using Gaussian Elimination until I hit a road bump:

3, 0, 6, 1, 0, 0;

0, -2, x-3, 1/3, 1, 0;

0, 0, x-5, 0, 0, 1;

Should I just keep on pushing though? Or should I try to figure X out? Or is there some sort of theorem out there than can help me?