Question

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

Answer 1

`-98`

Explanation:

`((color(teal)(3),color(teal)(1),color(teal)(-2),color(teal)(1)),(color(orange)(1),color(orange)(1),color(orange)(-3),color(orange)(2)),(2,0,2,3),(color(turquoise)(3),color(turquoise)(3),color(turquoise)(1),color(turquoise)(-3)))=`
`->` row2 `-` row1 `->` row2
`->` row4 `-3*` row1 `->` row4

`=((color(gray)(3),color(blue)(1),color(gray)(-2),color(gray)(1)),(-2,color(gray)(0),-1,1),(2,color(gray)(0),2,3),(-6,color(gray)(0),7,-6))`

`=1*(-1)^(1+2)*((-2,-1,1),(2,2,3),(-6,7,-6))`
`=-[24+18+14-(cancel(-12)-42+cancel(12))]`
`=-56-42=-98`