NCERT Solutions for class 12 Types of Matrices

NCERT Solutions for class 12 Types of Matrices

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 [a_ij]_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 .

  is a column matrix having one column and three rows.

are column matrices since they have only one column.

In general [a_ij]_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

is a matrix of order 2×2.Here m = n =2 and thus it is a square matrix.

are examples of square matrices.

In square matrices the entries a_11, a_22, a_33, a_44,…….., a_nn  are known as diagonal elements.

In the matrix

3, 7, 0  are diagonal elements.

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

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

Eg

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

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 I_n where n is ordered.

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

Eg

We denote this matrix by O.

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