Question

You are asked to construct a distance chart representing distances between cities given in a set with all the cities of the same set. What kind of matrix will come out of it?

• A. Rectangular matrix
• B. Square matrix
• C. Identity matrix
• D. Null matrix

Answer 1

The correct option is B

Square matrix

You are given a distance chart. You can see that the cities are listed above rows and columns. Each element in that corresponding row and column will represent the distance between those cities present in corresponding row and column. You can see an example below in which distances between 3 cities are given as described above.

$\begin{array}{ccc}& & \\ Delhi& Mumbai& Chennai\end{array}\begin{array}{c}\\ Delhi\\ Chennai\\ Mumbai\end{array}\left[\begin{array}{cccccccccccc}0& & & & & a& & & & & & b\\ a& & & & & 0& & & & & & c\\ b& & & & & c& & & & & & 0\end{array}\right]$

Invariably all diagonal elements will be zeroes and the chart will give a square matrix since

Number of rows = Number of columns.