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JAMB Mathematics 2011 Paper

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Question : 21

Total: 46

If

\begin{vmatrix} 2 & 3 \\ 5 & 3x \end{vmatrix} = \begin{vmatrix} 4 & 1 \\ 3 & 2x \end{vmatrix}

, find the value of x.

-6
6
-12
12

Solution:

Concept:

The determinant of a

2 \times 2

matrix

\begin{vmatrix} a & b \\ c & d \end{vmatrix}

is

ad - bc

.

Explanation:

Find the determinant of each matrix and set them equal.

Left determinant:

(2)(3x) - (3)(5) = 6x - 15

.

Right determinant:

(4)(2x) - (1)(3) = 8x - 3

.

Equate both sides:

6x - 15 = 8x - 3

.

Collect like terms:

6x - 8x = 15 - 3

.

Simplify:

-2x = 12

.

Divide both sides by

-2

:

x = \frac{12}{-2} = -6

.

Answer:

x = -6

, so the correct option is A.

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