Finding the Determinant of a 3 × 3 Matrix

Find the determinant of the 3 × 3 matrix given

A = [\begin{matrix} 0 & 2 & 1 \\ 3 & - 1 & 1 \\ 4 & 0 & 1 \end{matrix}]

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Augment the matrix with the first two columns and then follow the formula. Thus,

$\begin{array}{l} | A | = | \begin{matrix} 0 & 2 & 1 \\ 3 & - 1 & 1 \\ 4 & 0 & 1 \end{matrix} | \begin{matrix} 0 \\ 3 \\ 4 \end{matrix} \begin{matrix} 2 \\ - 1 \\ 0 \end{matrix} | \\ = 0 (- 1) (1) + 2 (1) (4) + 1 (3) (0) - 4 (- 1) (1) - 0 (1) (0) - 1 (3) (2) \\ = 0 + 8 + 0 + 4 - 0 - 6 \\ = 6 \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the determinant of the 3 × 3 matrix.

\det (A) = | \begin{matrix} 1 & - 3 & 7 \\ 1 & 1 & 1 \\ 1 & - 2 & 3 \end{matrix} |

How did it go?