Question:
For which value of x, are the determinants
\[
\begin{vmatrix}
2x & -3 \\
5 & x
\end{vmatrix}
\text{and}
\begin{vmatrix}
10 & 1 \\
-3 & 2
\end{vmatrix}
\text{ equal?}
\]
For which value of x, are the determinants
\[
\begin{vmatrix}
2x & -3 \\
5 & x
\end{vmatrix}
\text{and}
\begin{vmatrix}
10 & 1 \\
-3 & 2
\end{vmatrix}
\text{ equal?}
\]
Show Hint
Always expand determinant properly: $ad - bc$ for 2x2.
Updated On: Jul 1, 2025
- $\pm 3$
- $-3$
- $\pm 2$
- $2$
Show Solution
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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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