Chapter 7.2, Problem 1E

Solution

To find: The order of the given matrix and explain that whether the matrix is square matrix or not.

  $\left[\begin{array}{ccc}2& 3& -1\\ 1& 0& 5\end{array}\right]$

The order of the matrix is $2\times 3$ and it is not square matrix.

Given Information:

The matrix is defined as,

  $\left[\begin{array}{ccc}2& 3& -1\\ 1& 0& 5\end{array}\right]$

Concept Used:

Suppose that if $m$ and $n$ are two positive integers. A $m\times n$ is a rectangular array of m horizontal rows and n vertical columns of real numbers.

  $\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right]$

The short hand notation to express the matrix is $\left[a_{ij}\right]$ . Where, $i$ is row and $j$ is column.

A matrix is said to square matrix if and only if the row and the column of the matrix are equal.

Explanation:

Consider the given matrix,

  $\left[\begin{array}{ccc}2& 3& -1\\ 1& 0& 5\end{array}\right]$

It can observed that the matrix have 2 rows and 3 column. So the order of the matrix is $2\times 3$ .

As the row and column of the matrix are not equal. So it is not the square matrix.

Hence, the required order is $2\times 3$ and it is not the square matrix.