Question

How do you find the determinant of `((2, 5, -3, -1), (3, 0, 1, -3), (-6, 0, -4, 9), ( 4, 10, -4, -1))`?

Answer 1

`120`

Explanation:

`((color(teal)(2),color(teal)(5),color(teal)(-3),color(teal)(-1)),(3,0,1,-3),(-6,0,-4,9),(color(turquoise)(4),color(turquoise)(10),color(turquoise)(-4),color(turquoise)(-1)))=`
`->` row4 `-2*` row1 `->` row4

`=((color(gold)(2),color(blue)(5),color(gold)(-3),color(gold)(-1)),(3,color(gold)(0),1,-3),(-6,color(gold)(0),-4,9),(0,color(gold)(0),2,1))`

`=5*(-1)^(1+2)*((3,1,-3),(-6,-4,9),(0,2,1))`

`=-5[-12+36-(54-6)]`
`=-5[24-48]=5*24=120`