Question:
If \(\begin{vmatrix} 2x & 5 \\ 12 & x \end{vmatrix} = \begin{vmatrix} 6 & -5 \\ 4 & 3 \end{vmatrix}\), then the value of x is:
यदि \(\begin{vmatrix} 2x & 5 \\ 12 & x \end{vmatrix} = \begin{vmatrix} 6 & -5 \\ 4 & 3 \end{vmatrix}\) है, तो x का मान क्या है?
Options:
- \(\pm 3\)
- 7
- 3
- \(\pm 7\)
- \(\pm 3\)
- 7
- 3
- \(\pm 7\)
Correct Answer: d)
Explanation:
\(\det \begin{bmatrix} 2x & 5 \\ 12 & x \end{bmatrix} = 2x^2 – 60\).
\(\det \begin{bmatrix} 6 & -5 \\ 4 & 3 \end{bmatrix} = 18 – (-20) = 38\).
\(2x^2 – 60 = 38 \implies 2x^2 = 98 \implies x^2 = 49 \implies x = \pm 7\).
\(2x^2 – 60 = 18 – (-20) = 38 \implies 2x^2 = 98 \implies x^2 = 49 \implies x = \pm 7\)।