Determine Whether Matrix is Symmetric or Skew-Symmetric
Given:
\[ a_{ij} = i^2 – j^2 \]
Step 1: Find aji
\[ a_{ji} = j^2 – i^2 = -(i^2 – j^2) \]
Step 2: Compare
\[ a_{ji} = -a_{ij} \]
Conclusion:
\[ A^T = -A \]
Hence, the matrix is skew-symmetric.
\[ a_{ij} = i^2 – j^2 \]
\[ a_{ji} = j^2 – i^2 = -(i^2 – j^2) \]
\[ a_{ji} = -a_{ij} \]
\[ A^T = -A \]
Hence, the matrix is skew-symmetric.