AP EAMCET · Maths · Matrices
If \(k\) is one of the roots of the equation \(x^2-25 x+24=0\) such that \(A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 2 & 3 \\ 1 & 1 & k\end{array}\right]\) is a non-singular matrix, then \(A^{-1}=\)
- A \(-\frac{1}{46}\left[\begin{array}{ccc}90 & -94 & 8 \\ -138 & 46 & 0 \\ 2 & 2 & -8\end{array}\right]\)
- B \(-\frac{1}{92}\left[\begin{array}{ccc}45 & -47 & 4 \\ -69 & 23 & 0 \\ 1 & 1 & -4\end{array}\right]\)
- C \(-\frac{1}{46}\left[\begin{array}{ccc}45 & -47 & 4 \\ -69 & 23 & 0 \\ 1 & 1 & -4\end{array}\right]\)
- D \(-\frac{1}{92}\left[\begin{array}{ccc}90 & -94 & 8 \\ -138 & 46 & 0 \\ 2 & 2 & -8\end{array}\right]\)
Answer & Solution
Correct Answer
(B) \(-\frac{1}{92}\left[\begin{array}{ccc}45 & -47 & 4 \\ -69 & 23 & 0 \\ 1 & 1 & -4\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} x^2-25 x+24 & =0 \\ x^2-x-24 x+24 & =0 \\ x(x-1)-24(x-1) & =0 \\ (x-1)(x-24) & =0 \Rightarrow x=1,24 \end{aligned} \] \(\because k\) is one of the root of the Eq. (i),…
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