Question:

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

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Always expand determinant properly: $ad - bc$ for 2x2.
  • $\pm 3$
  • $-3$
  • $\pm 2$
  • $2$
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The Correct Option is A

Solution and Explanation

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) $\pm 2$.
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