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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
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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
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The correct answer is:
12
12
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 $=3+9=12$
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 $=3+9=12$
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