The value of $x$ such that the matrix $\left[\begin{array}{lll}x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 &…

The value of $x$ such that the matrix $\left[\begin{array}{lll}x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5\end{array}\right]$ is not invertible is
  1. $\frac{-10}{7}$
  2. $\frac{7}{10}$
  3. $\frac{-7}{10}$
  4. $\frac{10}{7}$

Solution

For given matrix to be invertible, we write $\begin{array}{l} \left|\begin{array}{lll} x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5 \end{array}\right|=0 \\ x(25-18)-2(20-12)+3(12-10)=0 \Rightarrow 7 x-16+6=0 \Rightarrow x=\frac{10}{7} \end{array}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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