This document is a lecture by Dr. Mehar Chand on the topics of addition and subtraction of matrices. It defines addition of matrices as combining matrices of the same order by adding corresponding elements. Scalar multiplication is defined as multiplying every element of a matrix by a scalar or number. The negative of a matrix is defined as multiplying every element by -1. Difference of matrices is defined as subtracting corresponding elements of matrices of the same order. The document provides definitions and examples for each topic and concludes by providing a link to a full video lecture on the subject.

1. Addition and
Subtraction of
Matrices
Dr. Mehar
Chand
Addition of
Matrices
Scalar
Multiplication
Negative of a
Matrix
Difference of a
Matrix
Video
Tutorial-III: Matrices
Basic Mathematics: Addition and
Subtraction of Matrices
Dr. Mehar Chand
Department of Mathematics
Baba Farid College, Bathinda-151001
April 22, 2020
Dr. Mehar Chand Addition and Subtraction of Matrices

2. Addition and
Subtraction of
Matrices
Dr. Mehar
Chand
Addition of
Matrices
Scalar
Multiplication
Negative of a
Matrix
Difference of a
Matrix
Video
Contents
1 Addition of Matrices
2 Scalar Multiplication
3 Negative of a Matrix
4 Difference of a Matrix
5 Full video Lecture
Dr. Mehar Chand Addition and Subtraction of Matrices

3. Addition and
Subtraction of
Matrices
Dr. Mehar
Chand
Addition of
Matrices
Scalar
Multiplication
Negative of a
Matrix
Difference of a
Matrix
Video
Addition of Matrices
Definition (Addition of Matrices)
Let A = [aij ]m×n and B = [bij ]m×n be two matrices of the
same order. Then their sum A + B is defined as a new
matrix C = [cij ]m×n, where cij = aij + bij for all 1 ≤ i ≤ m
and 1 ≤ j ≤ n
Dr. Mehar Chand Addition and Subtraction of Matrices

4. Addition and
Subtraction of
Matrices
Dr. Mehar
Chand
Addition of
Matrices
Scalar
Multiplication
Negative of a
Matrix
Difference of a
Matrix
Video
Scalar Multiplication
Definition (Scalar Multiplication)
Let A = [aij ]m×n be any matrix and k by any number or
scalar. Then the matrix obtained by multiplication of every
element of A by k is called a scalar multiplication and is
denoted by kA thus kA = [kaij ]m×n
Dr. Mehar Chand Addition and Subtraction of Matrices

5. Addition and
Subtraction of
Matrices
Dr. Mehar
Chand
Addition of
Matrices
Scalar
Multiplication
Negative of a
Matrix
Difference of a
Matrix
Video
Negative of a Matrix
Definition (Negative of a Matrix)
Let A = [aij ]m×n be any matrix, then negative of matrix A is
denoted by −A and is defined as (−1)A. Thus if
A = [aij ]m×n, then, −A = [−aij ]m×n
Dr. Mehar Chand Addition and Subtraction of Matrices

6. Addition and
Subtraction of
Matrices
Dr. Mehar
Chand
Addition of
Matrices
Scalar
Multiplication
Negative of a
Matrix
Difference of a
Matrix
Video
Difference of a Matrix
Definition (Difference of a Matrix)
Let A = [aij ]m×n and B = [bij ]m×n be two matrices of the
same order. Then their difference A − B is defined as a new
matrix C = [cij ]m×n, where cij = aij − bij for all 1 ≤ i ≤ m
and 1 ≤ j ≤ n
Dr. Mehar Chand Addition and Subtraction of Matrices

7. Addition and
Subtraction of
Matrices
Dr. Mehar
Chand
Addition of
Matrices
Scalar
Multiplication
Negative of a
Matrix
Difference of a
Matrix
Video
Full video Lecture
To see full video lecture visit the below link
https://youtu.be/hEId2ZuD4Qc
Dr. Mehar Chand Addition and Subtraction of Matrices

8. Addition and
Subtraction of
Matrices
Dr. Mehar
Chand
Addition of
Matrices
Scalar
Multiplication
Negative of a
Matrix
Difference of a
Matrix
Video
Thank you
Dr. Mehar Chand Addition and Subtraction of Matrices