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Calculate the determinant of the matrix:...

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lienetom | Student | eNoter

Posted February 28, 2012 at 2:37 AM via web

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Calculate the determinant of the matrix: `[[2,2-1,2+2,2-3],[2,2-2,2+1,2-1],[1,1+1,1+4,1-2],[0,0-3,0-1,0+1]]`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 28, 2012 at 3:09 AM (Answer #3)

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The determinant of `[[2,2-1,2+2,2-3],[2,2-2,2+1,2-1],[1,1+1,1+4,1-2],[0,0-3,0-1,0+1]]` has to be determined.

`[[2,2-1,2+2,2-3],[2,2-2,2+1,2-1],[1,1+1,1+4,1-2],[0,0-3,0-1,0+1]]`

=> `[[2,1,4,-1],[2,0,3,1],[1,2,5,-1],[0,-3,-1,1]]`

=>`2*[[0,3,1],[2,5,-1],[-3,-1,1]] - 2*[[1,4,-1],[2,5,-1],[-3,-1,1]] + 1*[[1,4,-1],[0,3,1],[-3,-1,1]] - 0`

=> `2*[[0,3,1],[2,5,-1],[-3,-1,1]] - 2*[[1,4,-1],[2,5,-1],[-3,-1,1]] + 1*[[1,4,-1],[0,3,1],[-3,-1,1]] - 0`

=> `2*(-3*(2 - 3) + 1(-2 + 15)) - 2*(5 -1) + 8*(2 - 3) `

`+ 2*(-2 + 15) + 1(3 + 1) - 4(0 + 3) - 1(0 + 9)`

=> 6 + 26 - 8 - 8 + 26 + 4 - 12 - 9

=> 25

The required determinant is 25.

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