Operations on Matrices
In this section, we shall discuss the addition and subtraction of matrices, multiplication of a matrix by a scalar and multiplication of matrices.
Two matrices can be added or subtracted if they have the same order. To add or subtract two matrices, simply add or subtract the corresponding elements.
If A = (aij ) , B = (bij ) , i = 1, 2, ... m , j = 1, 2, ... n then C = A + B is such that C = (cij ) where cij = a ij +bij for all i = 1, 2, ... m and j = 1, 2, ... n
Two examinations were conducted for three groups of students namely group 1, group 2, group 3 and their data on average of marks for the subjects Tamil, English, Science and Mathematics are given below in the form of matrices A and B. Find the total marks of both the examinations for all the three groups.
The total marks in both the examinations for all the three groups is the sum of the given matrices.
It is not possible to add A and B because they have different orders.
We can multiply the elements of the given matrix A by a non-zero number k to obtain a new matrix kA whose elements are multiplied by k. The matrix kA is called scalar multiplication of A.
Thus if A = (aij )m ×n then , kA = (kaij )m ×n for all i = 1,2,…,m and for all j = 1,2,…,n.
If A = then Find 2A+B.
Since A and B have same order 3 ×3 , 2A + B is defined.
Since A, B are of the same order 3 ×3 , subtraction of 4A and 3B is defined.