Question

Maximum number of different elements in a symmetric matrix of order n?

Answer 1

Answer:

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For a skew symmetric matrix , as we know all the diagonal elements are zero and the upper triangular elements are the same as that of lower triangular elements in such a fashion that the matrix A = -(transpose A) satisfies.

therefore , for a matrix A of dimension n *n , the diagonal elements are zero i.e there would be n zeros in the diagonal

therefore

no. of elements remaining to be distinct = total no. of elements -

diagonal elements

= (n * n ) - n

= n2 - n

Now as we already said that the the upper traingular half elements are same as that of lower triangular half.

therefore the maximum number of distinct elements are

= (n2 - n) /2

=(n ( n - 1) ) / 2

Answer 2

Answer:

Step-byjk-step explanation: