In this section, we shall discuss the addition and subtraction of matrices, multiplication of a matrix by a scalar and multiplication of matrices.

**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.

For example

If *A* = (*a _{ij}* ) ,

**Example 3.58**

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.

*Solution*

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* = (*a _{ij}* )

If A = then Find 2A+B.

Since *A* and *B* have same order 3 ×3 , 2*A* + *B*
is defined.

**Example
3.61**

*Solution*

Since *A, B* are of the same order 3 ×3 , subtraction of 4*A*
and 3*B* is defined.

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