Cofactor Expansion 4x4 linear algebra

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Compute the determinant by cofactor expansions.

 | 1 -2 5 2| | 0 0 3 0| | 2 -4 -3 5| | 2 0 3 5|

I figured the easiest way to compute this problem would be to use a cofactor across row 2. So I got:

det A =

 |-1 -2 2| -3| 2 -4 5| | 2 0 5|

I went on to factor across the third row.

det A =

 ( |-2 2| |-1 -2|) -3(2|-4 5| + 5| 2 -4|)

det A = -3(2(-10+8)+5(4+4))

det A = -3(-4+40)

det A = -108

When I check my work on a determinate calculator I see that I should be getting det A = 12, but I can't seem to see where I'm messing up.

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1 Answer

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The top left entry on the second matrix got copied wrong, it should be 1 not -1.

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