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:}

• A. $x=3, y=1$
• B. $x=1, y=3$
• C. $x=2, y=3$
• D. $x=1, y=1$

Hint:

Equal matrices = Equal positions. Just solve the resulting simple algebra.

Answer 1

The Correct Option is A

Step 1: Concept
Two matrices are equal if their corresponding elements are equal.

Step 2: Meaning
We can set up a system of linear equations by equating the elements at $(1,1)$ and $(2,2)$.

Step 3: Analysis
$x + y = 4$ and $x - y = 2$. Adding the two equations: $2x = 6 \implies x = 3$. Substituting $x=3$ into the first equation: $3 + y = 4 \implies y = 1$.

Step 4: Conclusion
The values are $x=3$ and $y=1$.
Final Answer: (A)