Question:
If $\begin{vmatrix}2x& 5 \\ 8 & x\end{vmatrix}=\begin{vmatrix}6 &-2 \\ 7& 3\end{vmatrix}$ then the value of $x$ is
If $\begin{vmatrix}2x& 5 \\ 8 & x\end{vmatrix}=\begin{vmatrix}6 &-2 \\ 7& 3\end{vmatrix}$ then the value of $x$ is
Show Hint
Unlike matrices, determinants are values. Expand both sides fully before trying to isolate the variable.
Updated On: May 5, 2026
- 3
- $\pm 6$
- -3
- +2
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Concept
To solve for $x$, we evaluate the determinants on both sides of the equation.
Step 2: Meaning
For a $2 \times 2$ matrix, the determinant is calculated as $(ad - bc)$.
Step 3: Analysis
Left side: $(2x \cdot x) - (5 \cdot 8) = 2x^2 - 40$. Right side: $(6 \cdot 3) - (-2 \cdot 7) = 18 + 14 = 32$. Equating both: $2x^2 - 40 = 32 \implies 2x^2 = 72 \implies x^2 = 36$.
Step 4: Conclusion
Taking the square root gives $x = \pm 6$.
Final Answer: (B)
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