Question

Let \[ A= \begin{pmatrix} 1 & x & 2x \\ 1 & 3x & 5x \\ 1 & 3 & 4 \end{pmatrix}, \qquad x\neq0. \] If \(\det(A)=0\), then \(x=\)

• A. \(-2\)
• B. \(-1\)
• C. \(1\)
• D. \(\dfrac12\)

Hint:

Whenever a question states \[ \boxed{\det(A)=0} \] compute the determinant carefully and solve the resulting algebraic equation. Also check whether any given restriction (such as \(x\neq0\)) eliminates one of the roots.

Answer 1

The Correct Option is B