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## Linear Algebra, Find the Determinant

Find the determinant of C by first row reducing it to a matrix with first column 1,0,0,0. Show the row operations and explain how all this tells you the value of the determinant of C when you are done.

C=(2,0,-6,8;3,1,0,3;-5,1,7,-8;0,0,5,1) where ; indicates a new row.
We're suppose to use the theorem DET(Ek)DET(Ek-1)...DET(E1)DET(A)=DET(C)

The problem that I'm having is that I know the determinate of C is -244 (calculator). But when I use the theorem I get (1/2)(1)(1)(-144) for the determinant. It really appears to be the first row operations, if it was 2 instead of 1/2 it'd work. I can't figure out how to resolve this, below is my work.

The first row operation I did was 1/2R1->R1, then -3R1+R2->R2, and finally 5R1+R3->R3. This left me with the matrix
A=(1,0,-3,4;0,1,9,-9;0,1,-8,12;0,0,5,1)
Hence the (1/2)(1)(1)(-144) for the determinant.

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