If the matrix \(\begin{bmatrix}2 & 1 & 3\\ 4 & x & 6\\ 1 & 2 & 1\end{bmatrix}\) is singular, then the value of x is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2
A matrix is singular when its determinant is zero. Expanding along the first row:
\( \Delta = 2(x \cdot 1 - 6 \cdot 2) - 1(4 \cdot 1 - 6 \cdot 1) + 3(4 \cdot 2 - x \cdot 1) \)
\( = 2x - 24 + 2 + 24 - 3x \)
\( = 2 - x \)
Setting \(\Delta = 0\):
\( 2 - x = 0 \)
\( x = 2 \)
Check: with x = 2 the second row (4, 2, 6) is twice the first row (2, 1, 3), so the determinant is indeed zero.