Class 12 Maths - Types Of Matrices (#class12Maths)(#cbse2021)(#cbsenotes)(#eduvictors)

Class 12 Maths - Types Of Matrices 

(1) Row matrix

If in a matrix, there is only one row, then it is called a Row Matrix. 

Thus $ A[a_{ij}]_{m \times n} $ is a row matrix if m = 1

e.g. [1 3 6] is a row matrix of order 1 × 3

(2) Column Matrix

A matrix which contains only one column, is called a column matrix. Thus $A[a_{ij}]_{m \times n}$ is a column matrix if n = 1.

e.g. $\begin{bmatrix} 5\\6 \\9 \end{bmatrix}$

(3) Square matrix

If number of rows and number of column in a matrix are equal, then it is called a square matrix. Thus $A[a_{ij}]_{m \times n}$ is a square matrix if m = n.

e.g. $\begin{bmatrix} 5 &6 \\7  & 8 \end{bmatrix}$

(4) Singleton matrix

A matrix having only one element, is called singleton matrix. Thus $A[a_{ij}]_{m \times n}$ is a singleton matrix if m = n = 1.

eg. [3], [7], [d], [–7] are singleton matrices.

(5) Null or zero matrix

If in a matrix all the elements are zero then it is called a zero matrix and it is generally denoted by O. Thus $A[a_{ij}]_{m \times n}$ is a zero matrix if $_{aij}=0$ for all i and j.

e.g. $\begin{bmatrix}0 & 0\\ 0 & 0\end{bmatrix}$

6) Diagonal matrix :

If all elements except the principal diagonal in a square matrix are zero, it is called a diagonal matrix. Thus a square matrix A[a_{ij}]_{m \times n}$ is a diagonal matrix if $a_{ij} = 0$, when i ≠ j.

e.g. $\begin{bmatrix}2 & 0 & 0\\ 0 & 3 & 0\\ 0 & 0 & 4\end{bmatrix}$ is a diagonal matrix of order 3 × 3, which also can be denoted by diag [2 3 4]

(7) Scalar Matrix :

If all the elements of the diagonal of a diagonal matrix are equal, it is called a scalar matrix. Thus a square matrix $A[a_{ij}]$ is a scalar matrix if

$a_{ij} = \left\{\begin{matrix}0 & i \neq  j \\ k & i = j \end{matrix}\right.$

where k is a constant.

e.g. $\begin{bmatrix}3 & 0\\ 0 & 3 \end{bmatrix}$

(8) Unit Matrix (Identity Matrix)

If all elements of principal diagonal in a diagonal matrix are 1, then it is called unit matrix. A unit matrix of order n is denoted by $I_n$.

Thus a square matrix $A =[a_{ij}]$ is a unit matrix if,

$a_{ij} = \left\{\begin{matrix} 1 & i = j\\ 0 & i \neq j \end{matrix}\right.$

e.g. $I_3 = \begin{bmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{bmatrix}$

Note : Every unit matrix is a scalar matrix.

(9) Rectangular Matrix 

A matrix of order m × n, such that m ≠ n, is called rectangular matrix.

(10) Horizontal Matrix 

A matrix in which the number of rows is less than the number of columns, is called horizontal matrix.

👉See Also:

Special Mathematical Constants

Types of Vectors
Introduction to Matrices (Part-1) Q & A