Question

If a square matrix has a number of elements outside its main diagonal, 90 show that the matrix order is 10 x 10​

Answer 1

Suppose the matrix has dimensions n x n, so the number of elements in the matrix is n²

The many elements contained in the diagonal of this square matrix, of course, have many elements n

With the equation known that the number of elements outside the main diagonal is 90, then mathematically, it can be written:

Main non-diagonal = Total main elements - diagonal

Thus becoming:

90 = n² - n

Complete according to quadratic equations:

0 = n² - n - 90

0 = (n + 9) (n-10)

We know that n must be positive because it is a dimension, so that the value of n that satisfies is n = 10

Answer 2

the number of elements outside the main diagonal is 90

Main non-diagonal = Total main elements - diagonal

90 = n² - n

0 = n² - n - 90

0 = (n + 9) (n-10)