Answer
357.3k+ views
Hint: 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.
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.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)