Question:
If
\[
\begin{bmatrix}
x+y & 2
1 & x-y
\end{bmatrix}
=
\begin{bmatrix}
4 & 2
1 & 2
\end{bmatrix},
\]
then the values of \(x\) and \(y\) are:
If
\[
\begin{bmatrix}
x+y & 2
1 & x-y
\end{bmatrix}
=
\begin{bmatrix}
4 & 2
1 & 2
\end{bmatrix},
\]
then the values of \(x\) and \(y\) are:
Show Hint
When two matrices are equal, compare corresponding entries to form equations.
Updated On: May 7, 2026
- \(x=3,\ y=1\)
- \(x=1,\ y=3\)
- \(x=2,\ y=3\)
- \(x=1,\ y=1\)
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
Two matrices are equal if all their corresponding elements are equal.
Step 1: Compare corresponding elements of both matrices. \[ \begin{bmatrix} x+y & 2 1 & x-y \end{bmatrix} = \begin{bmatrix} 4 & 2 1 & 2 \end{bmatrix} \] From the first row and first column: \[ x+y=4 \quad \cdots (1) \] From the second row and second column: \[ x-y=2 \quad \cdots (2) \]
Step 2: Add equations (1) and (2). \[ (x+y)+(x-y)=4+2 \] \[ 2x=6 \] \[ x=3 \]
Step 3: Substitute \(x=3\) in equation (1). \[ 3+y=4 \] \[ y=1 \] Therefore, \[ \boxed{x=3,\ y=1} \]
Step 1: Compare corresponding elements of both matrices. \[ \begin{bmatrix} x+y & 2 1 & x-y \end{bmatrix} = \begin{bmatrix} 4 & 2 1 & 2 \end{bmatrix} \] From the first row and first column: \[ x+y=4 \quad \cdots (1) \] From the second row and second column: \[ x-y=2 \quad \cdots (2) \]
Step 2: Add equations (1) and (2). \[ (x+y)+(x-y)=4+2 \] \[ 2x=6 \] \[ x=3 \]
Step 3: Substitute \(x=3\) in equation (1). \[ 3+y=4 \] \[ y=1 \] Therefore, \[ \boxed{x=3,\ y=1} \]
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