Question

How do you find the determinant of `((5, 3, 1, 2), (0, 1, -1, 3), (2, 7, -4, 1), (3, 3, 5, -2))`?

Answer 1

`434`

Explanation:

`((5,color(teal)(3),color(orange)(1),color(turquoise)(2)),(0,color(teal)(1),color(orange)(-1),color(turquoise)(3)),(2,color(teal)(7),color(orange)(-4),color(turquoise)(1)),(3,color(teal)(3),color(orange)(5),color(turquoise)(-2)))=`
`->` column3 `+` column2 `->` column3
`->` column4 `-3*` column2 `->` column4

`=((5,color(gold)(3),4,-7),(color(gold)(0),color(blue)(1),color(gold)(0),color(gold)(0)),(2,color(gold)(7),3,-20),(3,color(gold)(3),8,-11))`

`=1*(-1)^(2+2)*((5,4,-7),(2,3,-20),(3,8,-11))`

`=-165-240-112-(-63-800-88)`
`=-517+951=434`