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Compute the determinant by cofactor expansions.

A=

   | 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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  • $\begingroup$ You changed the sign of the upper left element: in your matrix it is $\;1\;$ , but then you changed it to $\;-1\;$ . $\endgroup$
    – DonAntonio
    Jun 25, 2016 at 23:07

1 Answer 1

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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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