Question

For which value of x, are the determinants \[ \begin{vmatrix} 2x & -3 \\ 5 & x \end{vmatrix} \text{and} \begin{vmatrix} 10 & 1 \\ -3 & 2 \end{vmatrix} \text{ equal?} \]

• A. $\pm 3$
• B. $-3$
• C. $\pm 2$
• D. $2$

Hint:

Always expand determinant properly: $ad - bc$ for 2x2.

Answer 1

The Correct Option is A

First determinant: \[ |A| = 2x \cdot x - (-3)(5) = 2x^2 + 15. \] Second determinant: \[ |B| = 10 \cdot 2 - (1)(-3) = 20 + 3 = 23. \] Equate: \[ 2x^2 + 15 = 23 \implies 2x^2 = 8 \implies x^2 = 4 \implies x = \pm 2. \] Oops! So the options say $\pm 3$, but solving gives $\pm 2$. So the correct answer is (C) $\pm 2$.