Question

If the rank of the matrix $\begin{bmatrix}-1 &2&5\\\ 2&-4&a-4\\\ 1&-2&a+1\end{bmatrix}$ is 1, then the value of $a$ is

• A. -1
• B. 2
• C. -6
• D. 4

Answer 1

Answer: (C)

-6

Answer 2

Let
$A=\begin{vmatrix}-1&2&5\\\ 2&-4&a-4\\\ 1&-2&a+1\end{vmatrix}\sim\begin{vmatrix}-1&2&5\\\ 0&0&a+6\\\ 0&0&a+6\end{vmatrix}$
$\left[R_{2}\rightarrow R_{2}+2R_{1},R_{3}\rightarrow R_{3}+R_{1}\right]$
clearly rank of A is 1 if a = -6