Question

What is a null Matrix? Give an example.

Answer 1

Before moving to null matrix let us discuss what is matrix.
The matrix is a rectangular array of numbers or symbols which are generally arranged in rows and columns. The order of the matrix is defined as the number of rows and columns.
The plural of matrix is matrix.
Null matrix is one of the types of matrix.

Complete step-by-step solution:
Null matrix:
If in a matrix all the elements are zero then it is called a zero matrix and it is generally denoted by$0$. Thus,$A=\left[ {{a}_{ij}} \right]m\times n$is a zero-matrix. If${{a}_{ij}}=0$for all ‘I’ and ‘j’.
So there are two possible cases of null matrices.
Normal matrix
Square matrix
So a normal matrix can be a matrix of order$m\times n$. For example;
$\left[ \begin{matrix} 0 & 0 \\\ \end{matrix} \right]$is the$1\times 2$matrix.
$\left[ \begin{matrix} 0 \\\ 0 \\\ 0 \\\ \end{matrix} \right]$is the$3\times 1$matrix.
$\left[ \begin{matrix} 0 & 0 & 0 \\\ \end{matrix} \right]$is the$1\times 3$matrix.
Secondly, the square matrix is the matrix of order$m\times n$in which ‘m’ is equal to ‘n’. so we can say that the square matrix is of order$m\times m$. For example;
$\left[ \begin{matrix} 0 & 0 \\\ 0 & 0 \\\ \end{matrix} \right]$is the$2\times 2$ square matrix.
$\left[ \begin{matrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ \end{matrix} \right]$is the$3\times 3$ square matrix.
$\left[ \begin{matrix} 0 & 0 & 0 & 0 \\\ 0 & 0 & 0 & 0 \\\ 0 & 0 & 0 & 0 \\\ 0 & 0 & 0 & 0 \\\ \end{matrix} \right]$is the$4\times 4$square matrix.
The first matrix$0$is a$2\times 2$matrix with all the elements equal to zero and the second matrix$0$is a$3\times 3$matrix with all the elements equal to zero.

Note: Every zero matrix is a null matrix. That means the mode of the matrix will also be zero. But if we are asked that if the mode of the matrix is zero then it will be a null matrix then the answer is no. That any other matrix may have mode equal to zero.