The number of symmetric matrices of order 3, with all the entries from the set 0,1,2,,9, i…

Question

The number of symmetric matrices of order 3, with all the entries from the set $\{0,1,2,\dots,9\}$, is

Accepted Answer

A symmetric $3	imes3$ matrix $\begin{pmatrix}a&b&c\b&d&e\c&e&f\end{pmatrix}$ is determined by its 6 independent entries $a,b,c,d,e,f$, each freely chosen from $\{0,\dots,9\}$ (10 choices).

Number of matrices $=10^6$.

Solutions · 1