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Question
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.
Options
512
64
8
4
Solution
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is 64.
Explanation:
Let us form a symmetric matrix of 3 × 3 order.
`[(a, b, c),(b, d, e),(c, e, f)]`
To fill a, b, c, d, e, f, we have 2 choices either 1 or – 1.
So, number of symmetric matrices will be 26 = 64.
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