Question

The number of arbitrary elements in a skew-symmetric matrix of order 5 is

A) 18 B) 16 C) 12 D) 10​

Answer 1

Answer:

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Answer 2

Given: The order of a skew-symmetric matrix = 5

To find: The number of arbitrary elements in the matrix

Solution: A skew-symmetric matrix has arbitrary elements on one side with respect to the diagonal, and those elements determine the other triangle of the matrix.

Hence the formula for finding the number of arbitrary elements in a skew -symmetric matrix is given by (n² - n)/2 = n(n - 1)/2, where n is the order of the metrix.

Therefore, the required number of arbitrary elements

= n(n -1)/2

= 5(5 - 1)/2

= (5 × 4)/2

= 20/2

= 10

So the number of arbitrary elements in a skew-symmetric matrix of order 5 is 10.

Answer: Option D) 10