Question

A system of equations is given in the matrix form as $\begin{bmatrix} \alpha & 2 & 3 \\ 2 & 3 & -\alpha \\ 3 & 5 & \alpha+1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \\ 5 \end{bmatrix}$ where $\alpha$ is an integer. If the system of equations does not have a unique solution, then the value of $\alpha$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Hint:

For matrix determinant questions in competitive exams, if one root is a clear integer and the other is a fraction, the integer is almost always the intended answer.

Answer 1

The Correct Option is A