Question

To calculate the number of non-zero entries in the matrix \({M_R}\).

Short answer

The number of non-zero entries of \({M_{\bar R}}\) is \({n^2} - k\).

Step-by-step solution

Given data

That the matrix \({M_R}\) of the relation \(R\) has \(k\) non-zero entries ……(1)

Concept of Matrix

The matrix\({M_R}\)is obtained from the matrix\({M_R}\)interchanged by\(0\)and\(1\) ……(2)

Calculate the number of non – zero entries in \({M_R}\) 

From \((2)\), the number of non-zero entries in \({M_{\bar R}}\) is precisely the number of zeros in the matrix \({M_R}\) which is \({n^2} - k\).

So, the total number of entries in the square matrix of size \(n\) is \({n^2}\).

The number of non-zero entries of \({M_{\bar R}}\) is \({n^2} - k\).