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**1. The problem statement, all variables and given/known data**

I think I have broken maths. I am reducing a matrix to row echelon form to find the determinant. The matrix I will show is nearly in the desired form

**2. Relevant equations**

1 -3 -2 1

0 1 2 -1

0 0 1 -0.8

0 0 1 0

**3. The attempt at a solution**

As it stands, the determinant is 0.8. However subtracting the 4th row from the 3rd row changes the determinant to -0.8. I thought adding multiples of one row to another left the determinant unchanged. So why hasn't it? Thanks for answers.