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12th Maths Online NCERT Solutions – Types of Matrices

Class 12 Maths Online NCERT Solutions Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths

Class 12 Maths Online NCERT Solutions – Types of Matrices

Class 12 Maths : Takshila Learning is a great e-learning platform for Class 12th Maths students and ensures that learning is not restrained by place or by time. We offer Mathematics online classes for board exams designed by our experienced faculties. We also provide NCERT Maths solutions, question bank with solutions, and sample papers keeping in mind the latest pattern of question paper of Class 12 exams. On our website, regular updates, notifications, and articles are published for your help. Here, we will share important facts related to ‘Types of Matrices’ from CBSE Class 12 maths.

Row matrix: A matrix is said to be a row matrix if it has only one row.

Eg     [  1 5 2 ] 1×3  is a matrix with one row and three columns. So, it is a row matrix.

[  4 1/2 0 -3 ]1×4,  [  1 0 ] 1×3  are row matrices since they have only one row.
In general [aij]1×n is a row matrix of order 1×n.

Column matrix: A matrix is said to be a column matrix if it has only one column.

Eg .

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths  is a column matrix having one column and three rows.

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths are column matrices since they have only one column.

In general [aij]m×1 is a column matrix of order m×1.

Square matrix: A matrix is said to be square matrix if the number of rows is equal to the number of columns. Thus, an m × n matrix is said to be a square matrix if m = n and is known as a square matrix of order ‘m’ or ‘n’.

 

For the practice sets of Matrices & more, click on 12th Class Maths.

Eg

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Mathsis a matrix of order 2×2.Here m = n =2 and thus it is a square matrix.

 

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths

are examples of square matrices.

In square matrices the entries a11, a22, a33, a44,…….., ann  are known as diagonal elements.

In the matrix

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths3, 7, 0  are diagonal elements.

Diagonal matrix: A square matrix A= [aij]n×n  is said to be a diagonal matrix if all its non

diagonal elements are zero ie  aij  = 0 if  i ≠ j.

 

Eg

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths

All are diagonal matrices.

Note: There is no condition on the diagonal elements. They can be zero or non zero.

 

Scalar matrix: A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal or we can say that the nondiagonal elements are zero and the diagonal elements are equal.

Eg

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths

Identity Matrix: A scalar matrix in which diagonal elements are only 1 ie nondiagonal elements are zero and rest are one. We denote this matrix by In where n is ordered.

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths

Null Matrix or Zero Matrix:  A matrix in which all the elements are zero.

Eg

Class 12 Maths Online NCERT Solutions - Types of Matrices,CBSE class 12 maths,12th maths,NCERT Solution for Class 12 Maths

We denote this matrix by O.

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