NECO 2023 · Paper 1 · Q16

Matrices & determinants

Find the determinant of the matrix $\begin{pmatrix} 2 & 3 & 1 \\ 1 & 0 & 2 \\ 0 & 2 & 3 \end{pmatrix}$ .

Worked solution (try it first)

Expand along the first row, with signs $+ \; - \; +$ .
The first term is $2 \times (0 \times 3 - 2 \times 2) = -8$ .
The second term is $-3 \times (1 \times 3 - 2 \times 0) = -9$ .
The third term is $1 \times (1 \times 2 - 0 \times 0) = 2$ .
Add them: $-8 - 9 + 2 = -15$ , option A.

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