Chapter 7.2, Problem 7E

Solution

To find: The specified element $a_{13}$ of the given matrix.

  $\left[\begin{array}{cccc}-2& 0& 3& 4\\ 3& 1& 5& -1\\ 1& 4& -1& 3\end{array}\right]$

The specified element is $a_{13}=3$ .

Given Information:

The matrix is defined as,

  $\left[\begin{array}{cccc}-2& 0& 3& 4\\ 3& 1& 5& -1\\ 1& 4& -1& 3\end{array}\right]$ $\left[0\right]$

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,

  $\left[\begin{array}{cccc}-2& 0& 3& 4\\ 3& 1& 5& -1\\ 1& 4& -1& 3\end{array}\right]$

Write the general matrix of the given order $3\times 4$ .

  $\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\end{array}\right]$

So, it be observed that the required element $a_{13}$ is 3.

Hence, the required value is 3.