JAMB 2012 · UTME · Q23

Matrices & determinants

If $\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix} = \begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix}$ , find the value of $x$ .

Worked solution (try it first)

A $2 \times 2$ determinant is $ad - bc$ .
The left side is $5 \times 2 - 3x = 10 - 3x$ .
The right side is $3 \times 5 - 5 \times 4 = 15 - 20 = -5$ .
So $10 - 3x = -5$ .
Take 10 from both sides: $-3x = -15$ .
Divide by $-3$ : $x = 5$ , option C.

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