Question

Evaluate the determinant for the following matrix: -4 -4 -3

3 3 -5
-5 2 -5
A. 75
B. -203
C. -263
D. -152

Answer 1

A suitable calculator finds the determinant to be ...

... B. -203

_____

This can be calculated by hand by copying the first two columns to the right of the given matrix, then forming the sum of products of the downward diagonals and subtracting the sum of products of the upward diagonals.

... (-4)(3)(-5) +(-4)(-5)(-5) +(-3)(3)(2) -(-5)(3)(-3) -(2)(-5)(-4) -(-5)(3)(-4)

... = 60 -100 -18 -45 -40 -60

... = -203