CBSE Class 12 Mathematics Chapter 3 Matrices Revision Notes: With the 2023 board exams around the corner, the time to put down the books and begin revising the topics has come. Mathematics is a subject that requires consistent practice and regular revision. Towards the end of the session year, it’s advised to students to revise what they already know rather than focusing on learning new topics.
The CBSE Class 12 exams will commence from February 15, 2024, and the mathematics paper is scheduled on March 9. The third chapter in the Class 12 math books is Matrices. It’s an important chapter in the curriculum and holds considerable weightage in the final exam. You can check out the CBSE Class 12 Chapter 3 Matrices revision notes here, along with supporting study material like mind maps and multiple choice questions.
CBSE Class 12 Maths Chapter 3 Matrices Revision Notes
Basic Definitions and Summary:
Important Terms and Definitions:
Matrix: An ordered rectangular array of numbers or functions.
Matrix Order: A matrix having m rows and n columns is called a matrix of order m × n.
Row Matrix: A matrix of order having only one row and any number of columns.
Column Matrix: A matrix having only one column and any number of rows.
Rectangular Matrix: A matrix of order m x n, such that m ≠ n.
Horizontal Matrix: A matrix in which the number of rows is less than the number of columns
Vertical Matrix: A matrix in which the number of rows is greater than the number of columns.
Square matrix: A matrix of order m×n is called square matrix if m = n.
Zero matrix: A = [aij]m×n is called a zero matrix, if aij = 0 for all i and j.
Diagonal matrix: A square matrix [aij]m×n is said to be diagonal, if aij = 0 for i ≠ j.
Scalar matrix: A diagonal matrix A = [aij]m×n is said to be scalar, if aij = k for i = j.
Unit matrix (Identity matrix): A diagonal matrix A = [aij]n is a unit matrix, if aij = 1 for i = j.
A is a symmetric matrix if A′ = A.
A is a skew-symmetric matrix if A′ = –A.
Any square matrix can be represented as the sum of a symmetric and a skew-symmetric matrix.
If A and B are two square matrices such that AB = BA = I, then B is the inverse matrix of A and is denoted by A–1 and A is the inverse of B.
Inverse of a square matrix, if it exists, is unique.
Addition/Subtraction of Matrices
Addition and subtraction of Matrices is a simple process but you have to keep a few properties in mind.
For matrix multiplication, the method is not straightforward. It follows different rules for scalar and matrix multiplication.
*The order of two matrices should be same for addition or subtraction operations to be performed.
A = [aij]m x n and B = [bij]m x n
Then, A + B = [aij + bij]m x n
Properties:
- A+B = B+A
- (A+B) + C = A + (B+C)
- x(A+B) = xA+xB
- A + (-A) = 0
Scalar Multiplication
- x(A+B) = xA+xB
- xA = Ax
- (x1+x2)A = x1A+x2A
Matrix Multiplication
- AB ≠ BA
- (AB)C = A(BC)
- (B + C) = A.B + A.C
Matrix Transpose
If a matrix is obtained from any given matrix A, by interchanging rows and columns, it is called the transpose of A and is denoted by A’ or AT.
If A = [aij]mxn and A’ = [bij]nxm then bij = aji, ∀ i, j
Properties:
