COMEDK · Maths · 21. Matrices
If \(A=\left[\begin{array}{cc}x-2 & x+2 \\ -2 & 1\end{array}\right]\) is a singular matrix, then possible value of \(x\) is
- A 2
- B -2
- C \(\frac{3}{2}\)
- D \(\frac{-3}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{-3}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { }|A|=0 \quad[\because \text { matrix is singular }] \\ & \Rightarrow|A|=(x-2) \times 1-(-2)(x+2)=0 \\ & \Rightarrow \quad x-2+2 x+4=0 \Rightarrow 3 x+2=0 \\ & \Rightarrow \quad x=-\frac{3}{2}\end{aligned}\)
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