Question

How do you determine the order of the matrix \left[ {\begin{array}{*{20}{c}} { - 7}&6&4 \\\ 0&{ - 5}&1 \end{array}} \right]?

Answer 1

First find the number of rows and number of columns present in the matrix, then write the order of the matrix accordingly if a matrix has “m” number of rows and “n” number of columns then the order of the matrix is given by $m \times n$. You can check your answer by multiplying the terms of the order which should be equals to the number of elements present in the matrix.

Complete step by step solution:
Before finding the order of a matrix, let us understand first what is a matrix? It is sufficient to characterize matrix as a rectangular sequence of numbers or functions that are also known as matrix elements. It is 2 dimensional, since a matrix is a rectangular array. In essence, a two dimensional array consists of the number of rows denoted by m and the number of columns denoted by n.
Now coming to the question, how do we determine the order of the given matrix \left[ {\begin{array}{*{20}{c}} { - 7}&6&4 \\\ 0&{ - 5}&1 \end{array}} \right]
Order of a matrix having “m” number of rows and “n” number of columns is given as $m \times n$
So first we will find the number of rows $(m)$ and columns $(n)$ in the given matrix \left[ {\begin{array}{*{20}{c}} { - 7}&6&4 \\\ 0&{ - 5}&1 \end{array}} \right]
We can see in the given matrix that number of rows, $m = 2$ and number of columns, $n = 3$
$\therefore$ order of the matrix \left[ {\begin{array}{*{20}{c}} { - 7}&6&4 \\\ 0&{ - 5}&1 \end{array}} \right]\;{\text{is}}\;2 \times 3

Note: Number of horizontal lines is called rows in a matrix whereas number of vertical lines is known as columns in a matrix. The number of elements present in the matrix is always equal to the product of number rows and number of columns.