Question:
Let $A=\begin{pmatrix}0& 2\\ 3& 4\end{pmatrix}$ and $I=\begin{pmatrix}1& 0\\ 0& 1\end{pmatrix}$. If $(I+A)\begin{pmatrix}4&-3\\ 2&-1\end{pmatrix}=\begin{pmatrix}8&-5\\ 22& x\end{pmatrix}$, then the value of $x$ is equal to ________.
Let $A=\begin{pmatrix}0& 2\\ 3& 4\end{pmatrix}$ and $I=\begin{pmatrix}1& 0\\ 0& 1\end{pmatrix}$. If $(I+A)\begin{pmatrix}4&-3\\ 2&-1\end{pmatrix}=\begin{pmatrix}8&-5\\ 22& x\end{pmatrix}$, then the value of $x$ is equal to ________.
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To find $x$, only calculate the entry in the second row and second column.
Updated On: Jun 26, 2026
- 14
- -14
- 12
- -12
- 15
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Find the matrix $(I+A)$ and perform matrix multiplication.
Step 2: Meaning
$I+A = \begin{pmatrix}1& 0\\ 0& 1\end{pmatrix} + \begin{pmatrix}0& 2\\ 3& 4\end{pmatrix} = \begin{pmatrix}1& 2\\ 3& 5\end{pmatrix}$.
Step 3: Analysis
$\begin{pmatrix}1& 2\\ 3& 5\end{pmatrix} \begin{pmatrix}4&-3\\ 2&-1\end{pmatrix} = \begin{pmatrix} (4+4) & (-3-2) \\ (12+10) & (-9-5) \end{pmatrix} = \begin{pmatrix} 8 & -5 \\ 22 & -14 \end{pmatrix}$.
Step 4: Conclusion
Comparing with $\begin{pmatrix}8&-5\\ 22& x\end{pmatrix}$, we get $x = -14$. Final Answer: (B)
Find the matrix $(I+A)$ and perform matrix multiplication.
Step 2: Meaning
$I+A = \begin{pmatrix}1& 0\\ 0& 1\end{pmatrix} + \begin{pmatrix}0& 2\\ 3& 4\end{pmatrix} = \begin{pmatrix}1& 2\\ 3& 5\end{pmatrix}$.
Step 3: Analysis
$\begin{pmatrix}1& 2\\ 3& 5\end{pmatrix} \begin{pmatrix}4&-3\\ 2&-1\end{pmatrix} = \begin{pmatrix} (4+4) & (-3-2) \\ (12+10) & (-9-5) \end{pmatrix} = \begin{pmatrix} 8 & -5 \\ 22 & -14 \end{pmatrix}$.
Step 4: Conclusion
Comparing with $\begin{pmatrix}8&-5\\ 22& x\end{pmatrix}$, we get $x = -14$. Final Answer: (B)
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