📘 Question
If
\[
A =
\begin{bmatrix}
5 & x \\
y & 0
\end{bmatrix}
\]
and \(A = A^T\), find \(x\) and \(y\).
✏️ Step-by-Step Solution
Step 1: Use symmetric condition
\[
A = A^T
\]
So corresponding elements must be equal:
- \(x = y\)
Step 2: Final result
Thus, the only condition is:
\[
x = y
\]
✅ Final Answer
\[
\boxed{x = y}
\]
💡 Key Concept
A matrix is symmetric if:
\[
a_{ij} = a_{ji}
\]
So off-diagonal elements must be equal.