Question

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

Answer 1

-35

Explanation:

We can use a Laplace expansion in order to find the determinant.

`det((1, 3, 1), (2, 1, -5), (3, -1, -4))`
`= 1 * det((1,-5),(-1,-4)) -1 * 3 det((2,-5),(3,-4)) + 1 det((2,1),(3,-1))`
We know how to take the determinant of a 2x2 matrix, so we do that and simplify
`= 1(-4 - 5) - 3 (-8 - (-15)) + 1(-2 - 3)`
`= -9 - 21 - 5 = -35`