Question

How do you find the value of the determinant `|(6, 3, -1), (0, 3, 3), (-9, 0, 0)|`?

Answer 1

`abs((6, 3, -1),(0, 3, 3),(-9,0,0)) = -108`

Explanation:

I will use a couple of properties of the determinant:

• The determinant is unaltered when a multiple of one row is added to (or subtracted from) another row.

• The determinant of an upper ot lower triangular matrix is the product of the main diagonal.

Given:

`abs((6, 3, -1),(0, 3, 3),(-9,0,0))`

Subtract `"row2"` from `"row1"` to get:

`abs((6, 0, -4),(0, 3, 3),(-9,0,0))`

Add `3/2 xx "row1"` to `"row3"` to get:

`abs((6, 0, -4),(0, 3, 3),(0,0,-6))`

Since this is an upper triangular matrix, we can just multiply the diagonal to get the determinant:

`abs((color(blue)(6), 0, -4),(0, color(blue)(3), 3),(0,0,color(blue)(-6))) = 6*3*(-6) = -108`