If the determinant of the matrix \(\begin{pmatrix} 2 & x \\ 3 & 5 \end{pmatrix} = 13\), find the value of x.
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Correct Answer: Option B
Explanation:
\(\begin{pmatrix} 2 & x \\ 3 & 5 \end{pmatrix} = 13\)
\(\begin{vmatrix} 2 & x \\ 3 & 5 \end{vmatrix} = (2 \times 5) - (3 \times x) = 13\)
\(10 - 3x = 13 \implies -3x = 3; x = -1\)
\(\begin{pmatrix} 2 & x \\ 3 & 5 \end{pmatrix} = 13\)
\(\begin{vmatrix} 2 & x \\ 3 & 5 \end{vmatrix} = (2 \times 5) - (3 \times x) = 13\)
\(10 - 3x = 13 \implies -3x = 3; x = -1\)