Paragraph: Let $A$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either 0 or 1 …
Paragraph:
Let $A$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them are 0 .
Question:
The number of matrices in $A$ is
12
6
9
3
Solution
Case $I$ When all three diagonal elements are 1 , then
Number of matrices $={ }^3 C_1=3$
Case II When two diagonal elements are zero and one element is one no, then Number of matrices $={ }^3 C_1 \cdot{ }^3 C_1=9$
$\therefore$ Total matrices $=3+9=12$