Matrices and Determinants
Symmetric and Skew-Symmetric Matrices
Premium Question
Grade 12
Question:
The minimum number of distinct entries needed to completely specify a symmetric matrix of order $n$ is:
(1) $n^2$
(2) $\frac{n(n - 1)}{2}$
(3) $\frac{n(n + 1)}{2}$
(4) $2n - 1$
Step-by-Step Solution
Key Concept: In a symmetric matrix, every entry below the leading diagonal is forced to equal the corresponding entry above it — count the entries lying on or above the diagonal of an $n \times n$ grid.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)