Q74 / 120 · VITEEE 2007 · Mathematics

If the rank of the matrix $\left(\begin{array}{ccc}-1 & 2 & 5 \\ 2 & -4 & a-4 \\ 1 & -2 & a+1\end{array}\right)$ is 1, then the value of a is

  • A
    $-1$
  • B
    2
  • Correct answer
    C
    $-6$
  • D
    4

Solution

Let $\mathrm{A}=\left|\begin{array}{ccc} -1 & 2 & 5 \\ 2 & -4 & \mathrm{a}-4 \\ 1 & -2 & \mathrm{a}+1 \end{array}\right|-\left|\begin{array}{ccc} -1 & 2 & 5 \\ 0 & 0 & \mathrm{a}+6 \\ 0 & 0 & \mathrm{a}+6 \end{array}\right|$ $\left[\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}+2 \mathrm{R}_{1}, \mathrm{R}_{3} \rightarrow \mathrm{R}_{3}+\mathrm{R}_{1}\right]$ clearly rank of $A$ is 1 if $a=-6$

Hence, the correct answer is option: 'C'.

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