KCET · Maths · Matrices
If \(A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]\) is singular, then the possible values of \(x\) are
- A \(0,12,-12\)
- B \(0,1,-1\)
- C \(0,4,-4\)
- D \(0,5,-5\)
Answer & Solution
Correct Answer
(A) \(0,12,-12\)
Step-by-step Solution
Detailed explanation
We have, \(A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]\)
Since, \(A\) is singular.
\[
\begin{aligned}
& &|A| &=0 \\
\Rightarrow & & & \\
\Rightarrow & x\left[x^{2}-0\right]+16[9 x-0] &=0 \\
\Rightarrow &-x^{3}+144 x &=0 \\
\Rightarrow & x\left(x^{2}-144\right) &=0 \\
\Rightarrow & x &=0 \\
& \Rightarrow & x &=\pm 12
\end{aligned}
\]
Since, \(A\) is singular.
\[
\begin{aligned}
& &|A| &=0 \\
\Rightarrow & & & \\
\Rightarrow & x\left[x^{2}-0\right]+16[9 x-0] &=0 \\
\Rightarrow &-x^{3}+144 x &=0 \\
\Rightarrow & x\left(x^{2}-144\right) &=0 \\
\Rightarrow & x &=0 \\
& \Rightarrow & x &=\pm 12
\end{aligned}
\]
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