Chapter 11.CR, Problem 1CR

To determine

The matrix $\left[\begin{array}{cc}5& 7\\ 3& 9\\ 1& 0\end{array}\right]$ is a row matrix, a column matrix, a square matrix or neither.

Answer to Problem 1CR

Solution:

The matrix $\left[\begin{array}{cc}5& 7\\ 3& 9\\ 1& 0\end{array}\right]$ is neither row matrix, a column matrix nor a square matrix.

Explanation of Solution

Consider the given matrix,

$\left[\begin{array}{cc}5& 7\\ 3& 9\\ 1& 0\end{array}\right]$

A square matrix is a matrix that, have same number of rows and columns.

A column matrix is that matrix, which have only one column and a row matrix is a matrix that have only one row.

Since the given matrix is matrix of order $3\times 2$. Which mean it has $3$ rows and $2$ columns.

The given matrix is not having same number of rows and columns and the number of rows and columns both are more than one. So, the given matrix is neither row matrix column matrix nor square matrix.

Conclusion:

Hence, the matrix $\left[\begin{array}{cc}5& 7\\ 3& 9\\ 1& 0\end{array}\right]$ is neither row matrix a column matrix nor a square matrix.