Question:medium
Let \( A, B, C \) be three \( 2\times2 \) matrices with real entries such that
\[
B=(I+A)^{-1} \quad \text{and} \quad A+C=I.
\]
If
\[
BC=\begin{bmatrix}1 & -5 \\-1 & 2\end{bmatrix}
\quad \text{and} \quad
B\begin{bmatrix}x_1\\x_2\end{bmatrix}
=\begin{bmatrix}12\\-6\end{bmatrix},
\]
then \( x_1+x_2 \) is:
Let \( A, B, C \) be three \( 2\times2 \) matrices with real entries such that
\[
B=(I+A)^{-1} \quad \text{and} \quad A+C=I.
\]
If
\[
BC=\begin{bmatrix}1 & -5 \\-1 & 2\end{bmatrix}
\quad \text{and} \quad
B\begin{bmatrix}x_1\\x_2\end{bmatrix}
=\begin{bmatrix}12\\-6\end{bmatrix},
\]
then \( x_1+x_2 \) is:
Show Hint
In matrix problems, always try to eliminate variables using identities before directly computing inverses.
Updated On: Apr 1, 2026
- \(4\)
- \(0\)
- \(-2\)
- \(2\)
Show Solution
The Correct Option is D
Solution and Explanation
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