Question

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

Answer 1

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_11a_22 - a_12a_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#