WAEC 2017 · Paper 2 · Q9

Matrices & linear transformations

Given that $F = \begin{pmatrix} 3 & 4 & 2 \\ 0 & -1 & 2 \\ 2 & 1 & -2 \end{pmatrix}$ :

(a)
Find $|F|$ , the determinant of $F$ .
(b)
Use the determinant of $F$ to solve the system of equations $3x + 4y + 2z = -1$ , $-y + 2z = -8$ , $2x + y - 2z = 6$ simultaneously.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

Expand along the top row: $|F| = 3\big((-1)(-2) - 2(1)\big) - 4\big(0(-2) - 2(2)\big) + 2\big(0(1) - (-1)(2)\big)$ .
$= 3(0) - 4(-4) + 2(2) = 20$ .

(b)

Replace each column in turn by $-1, -8, 6$ : $\Delta_x = -20$ , $\Delta_y = 40$ and $\Delta_z = -60$ .
So $x = \dfrac{-20}{20} = -1$ , $y = \dfrac{40}{20} = 2$ and $z = \dfrac{-60}{20} = -3$ .
Check: $3(-1) + 4(2) + 2(-3) = -1$ ✓, $-2 + 2(-3) = -8$ ✓ and $2(-1) + 2 - 2(-3) = 6$ ✓.

Report a problem with this question