# How do you find the determinant of |(0,1,-4), (3,2,3), (8,-3,4)|?

Jan 18, 2017

Here is a reference that shows you how to evaluate a 3 x 3 determinant

#### Explanation:

Separate it into three 2 x 2 determinants with the coefficients of the top row multiplying the determinants alternating + and - signs:

| (0,1,-4), (3,2,3), (8,-3,4) | = + 0| (2,3), (-3,4) | - 1| (3, 3), (8,4) | + -4| (3,2), (8,-3) |

Use ${a}_{11} {a}_{22} - {a}_{12} {a}_{21}$ to evaluate the 2 x 2 determinants.

| (0,1,-4), (3,2,3), (8,-3,4) | = 0 - 1{(3)(4) - (3)(8)} - 4{(3)(-3) - (2)(8)}

| (0,1,-4), (3,2,3), (8,-3,4) | = 112