Question

The number of different nx n symmetric matrices with each elements being either 0 or 1 is​

Answer 1

Answer:

hi mate ,

In a symmetric matrix, the lower triangle must be the mirror image of upper triangle using the diagonal as mirror. Diagonal elements may be anything. Therefore, when we are counting symmetric matrices we count how many ways are there to fill the upper triangle and diagonal elements. Since the first row has n elements, second (n - 1) elements, third row ( n - 2) elements and so on upto last row, one element.  

Total number of elements in diagonal + upper triangle

Now, each one of these elements can be either 0 or 1. So total number of ways we can fill these elements is

Since there is no choice for lower triangleelements the answer is power (2, {n2 + n)/2).

hope this helps

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