JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let A, B and C be three \(2\times2\) matrices with real entries such that \(B=(I+A)^{-1}\) and \(A+C=I.\) If \(\mathrm{BC}=\left[\begin{array}{cc}1 & -5 \\ -1 & 2\end{array}\right]\) and \(\mathrm{CB}\left[\begin{array}{l}\mathrm{x}_1 \\ \mathrm{x}_2\end{array}\right]=\left[\begin{array}{l}12 \\ -6\end{array}\right]\), then \(x_1+x_2\) is
- A 2
- B \(0\)
- C -2
- D 4
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
\(B=(I+A)^{-1}, A+C=I\) \(\Rightarrow B(I+A)=(I+A)B=I\) \(\Rightarrow B+BA=B+AB\) \(\Rightarrow B+B(I-C)=B+(I-C)B\) \(\Rightarrow 2 \mathrm{B}-\mathrm{BC}=2 \mathrm{~B}-\mathrm{CB}\) \(\Rightarrow \mathrm{BC}=\mathrm{CB}\)…
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