MHT CET · Maths · Matrices
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
- A \(\frac{-10}{7}\)
- B \(\frac{7}{10}\)
- C \(\frac{-7}{10}\)
- D \(\frac{10}{7}\)
Answer & Solution
Correct Answer
(D) \(\frac{10}{7}\)
Step-by-step Solution
Detailed explanation
For given matrix to be invertible, we write
\(\left|\begin{array}{lll}x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5\end{array}\right|=0\)
\(x(25-18)-2(20-12)+3(12-10)=0 \Rightarrow 7 x-\) \(16+6=0 \Rightarrow x=\frac{10}{7}\)
\(\left|\begin{array}{lll}x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5\end{array}\right|=0\)
\(x(25-18)-2(20-12)+3(12-10)=0 \Rightarrow 7 x-\) \(16+6=0 \Rightarrow x=\frac{10}{7}\)
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