JAMB 2011 · UTME · Q25

Evaluate $\begin{vmatrix} 4 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \end{vmatrix}$ .

Worked solution (try it first)

Expand along the first row, with signs $+ \; - \; +$ .
The first term is $4 \times (3 \times 3 - (-1)(1)) = 4 \times 10$
$= 40$ .
The second term is $-2 \times (2 \times 3 - (-1)(-1)) = -2 \times 5$
$= -10$ .
The third term is $-1 \times (2 \times 1 - 3 \times (-1)) = -1 \times 5$
$= -5$ .
Add them: $40 - 10 - 5 = 25$ , option A.