Matrices & Determinants
Counting Symmetric Matrices
nta_pyq_2023_apr
Grade 12
Question:
The number of symmetric matrices of order 3, with all entries from $\{0,1,2,3,4,5,6,7,8,9\}$ is
$6^{10}$
$10^6$
$9^{10}$
$10^9$
Step-by-Step Solution
Key Concept: A $3\times3$ symmetric matrix has 6 independent entries: 3 diagonal ($a_{11},a_{22},a_{33}$) and 3 upper-triangular ($a_{12},a_{13},a_{23}$). Each has 10 choices.
$10^6$ symmetric matrices.
Correct Answer: 2