Q63 / 155 · WBJEE 2020 · Mathematics

Let $\mathrm{A}=\left(\begin{array}{ccc}12 & 24 & 5 \\ \mathrm{x} & 6 & 2 \\ -1 & -2 & 3\end{array}\right) .$ The value of $\mathrm{x}$ for which the matrix $\mathrm{A}$ is not invertible is

  • A
    6
  • B
    12
  • Correct answer
    C
    3
  • D
    2

Solution

Hint: If matrix is not invertible $\Rightarrow|\mathrm{A}|=0$ $\therefore|\mathrm{A}|=\left|\begin{array}{ccc}12 & 24 & 5 \\ \mathrm{x} & 6 & 2 \\ -1 & -2 & 3\end{array}\right|=0 \Rightarrow \mathrm{x}=3$

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

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