If $\begin{vmatrix}-x & 12 \\-1 & 4 \end{vmatrix} = - 12$, find x.

1. Analyze the question

You are given a $2 \times 2$ determinant equation and asked to solve for the unknown variable $x$. The determinant of a matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ is calculated as $(ad - bc)$.

2. Explain the concept

For any $2 \times 2$ matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$, the determinant is found by multiplying the elements of the leading diagonal ($a$ and $d$) and subtracting the product of the elements of the other diagonal ($b$ and $c$). Formula: Determinant = $(a \times d) - (b \times c)$

3. Show the solution

Given the matrix: $\begin{vmatrix} -x & 12 \\ -1 & 4 \end{vmatrix} = -12$

Step 1: Apply the determinant formula $(-x \times 4) - (12 \times -1) = -12$

Step 2: Simplify the expressions $-4x - (-12) = -12$ $-4x + 12 = -12$

Step 3: Isolate the term with $x$ Subtract 12 from both sides: $-4x = -12 - 12$ $-4x = -24$

Step 4: Solve for $x$ Divide both sides by -4: $x = \frac{-24}{-4}$ $x = 6$

4. Identify the answer

Comparing our result to the given options: A. -6 B. -2 C. 3 D. 6

The correct option is D.

5. Tip

When dealing with determinants involving negative signs, always use brackets for your multiplication. A common mistake in JAMB exams is forgetting that subtracting a negative number (like $-(-12)$) turns it into a positive addition ($+12$). Always double-check your signs!