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Prove determinate of matrix is 150

1 2 3 4

4 3 2 1

0 -1 2 3

1 6 4 -2

Prove determinate of matrix is 150

1 2 3 4

4 3 2 1

0 -1 2 3

1 6 4 -2

My solution is incorrect and maybe my method is incorrect but I cant figure it out. I went down the first column to make use of that zero.

Here is the basic method (a

_{ij})(-1)

^{ij}*Det(3x3) >> (a

_{ij})(-1)

^{ij}* (a

_{ij})(-1)

^{ij}*Det(2x2) where the second a

_{ij}and (-1)

^{ij}are for the newly created 3x3 matrix

First term:

(1)(-1)

^{2}(3)(-1)

^{2}[(2)(-2)-(4)(3)] = -48

Second term:

(4)(-1)

^{3}(2)(-1)

^{2}[(2)(-2)-(4)(3)] = 128

Third term = 0

Fourth term

(1)(-1)

^{5}(2)(-1)

^{2}[(2)(3)-(2)(1)] = -8

Det = -48 +128 - 8 = 72.