Operations On Matrices





In this page operations on matrices we are going to see how to add,subtract and multiply two matrices.

Addition of two matrices:

Two and more matrices can be added if and only if they are having same order. If the order those matrices are not same then we cannot add those matrices.

Example 1:

Find the sum of the following matrices

A =
 
0 2 7
-3 2 11
 
 
B =
 
-3 1 13
8 -7 0
 

Solution:

A+B=
 
0 2 7
-3 2 11
 
+
 
-3 1 13
8 -7 0
 
 

The given two matrices are in the same order, so we may add these matrices. For that we have to combine the corresponding terms.

                      
  =
 
0-3   2+1   7+13
-3+8   2-7   11+0
 
 
  =
 
-3   3   20
5   -5   11
 
 

Subtraction of two matrices:

Two and more matrices can be subtracted if and only if they are having same order. If the order those matrices are not same then we cannot subtract those matrices.

Example 2:

Subtract the following matrices

A =
 
5 -1 3
8 6 -3
 
 
B =
 
-4 0 -5
7 -8 11
 

Solution:

A-B=
 
5 -1 3
8 6 -3
 
-
 
-4 0 -5
7 -8 11
 
 

The given two matrices are in the same order, so we shall subtract these matrices. For that we have to combine the corresponding terms.

                      
  =
 
5-(-4)   -1-0   3-(-5)
8-7   6-(-8)   -3-11
 
 
                      
  =
 
5+4   -1   3+5
8-7   6+8   -3-11
 
 
  =
 
9   -1   8
1   14   -14
 
 

Multiplication of two matrices:

The product of matrix AB is determined by myltiplying every row matrix of A multiplying by the column matrix of B.

Example 3:

Multiply the following matrices

A =
 
5 -1
8 6
 
 
B =
 
-4 0
7 -8
 

Every column of the second is to be multiplied by every row of the first matrix.

AB=
 
5 -1
8 6
 
x
 
-4 0
7 -8
 
 


=
 
5 -1
 
x
 
-4
7
 
 
 
5 -1
 
x
 
0
-8
 


  
 
8 6
 
x
 
-4
7
 
 
 
8 6
 
x
 
0
-8
 

=
 
(-20-7) (0+8)
(-32+42) (0-48)
 

AB=
 
-27 8
10 -48
 

These are the properties of the topic operations on matrices.operations on matrices







Operations on Matrices to Matrix Introduction
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