Q58 / 160 · AP EAMCET 2007 · Mathematics

If $\left[\begin{array}{rrr}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix, then $x$ is equal to

  • A
    $0$
  • B
    $1$
  • Correct answer
    C
    $-3$
  • D
    $3$

Solution

Let $A=\left[\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix Then, $|A|=0$ $\begin{aligned} & \therefore \quad\left|\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right|=0 \\ & \Rightarrow 1[6-28]-2[-24-14]+x[16+2]=0 \\ & \Rightarrow \quad-22-2 \times(-38)+x \times 18=0 \\ & \Rightarrow \quad-22+76+18 x=0 \\ & \Rightarrow \quad x=-3 \\ & \end{aligned}$

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

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