Question

To calculate the matrix representation of the given relation on the set \(\{ 1,2,3,4\} \).

Short answer

The matrix is given as:

\(\left( {\begin{array}{*{20}{l}}0&1&1&1\\0&0&1&1\\0&0&0&1\\0&0&0&0\end{array}} \right)\)

Step-by-step solution

Given data

The relation defined by the ordered pairs \(\{ (1,2),(1,3),(1,4),(2,3),(2,4),(3,4)\} \) ……(1)

Concept of Matrix

The matrix entries are defined as follows:

\({(i,j)^{th}}\)entry is\(1\)if\(i\)is related to\(j\), otherwise\(0\).

Calculation of the matrix

The matrix corresponds to the relation (1) is the \(3 \times 3\) matrix whose entries are filled in accordance to the definition of matrix.

So, the matrix is given as:

\(\left( {\begin{array}{*{20}{l}}0&1&1&1\\0&0&1&1\\0&0&0&1\\0&0&0&0\end{array}} \right)\)