JAMB 2001 · UME · Q19

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

Worked solution (try it first)

Expand along the first row, with signs $+ \; - \; +$ .
The minor of the first entry is $1 \times 1 - 1 \times 2 = -1$ , so the first term is $(-1)(-1) = 1$ .
The minor of the second entry is $3 \times 1 - 1 \times 1 = 2$ .
With the minus sign, the term is $-(-1)(2) = 2$ .
The third term is $-1 \times (3 \times 2 - 1 \times 1) = -5$ .
Add them: $1 + 2 - 5 = -2$ , option B.