Adding Two Matrices





In this page adding two matrices we are going to see how to add two matrices with brief explanation.

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.


Question 1:

Find the sum of the following matrices

A =
 
1 3
7 4
 
 
B =
 
-3 1
8 -7
 

Solution:

A+B=
 
1 3
7 4
 
+
 
-3 1
8 -7
 
 

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

                      
  =
 
(1+(-3))   (3+1)
(7+8)   (4+(-7))
 
 
  =
 
-2   4
15   -3
 
 

Question 2:

Find the sum of the following matrices

A =
 
5 11
3 -2
 
 
B =
 
7 9
8 7
 

Solution:

A+B=
 
5 11
3 -2
 
+
 
7 9
8 7
 
 

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

                      
  =
 
(5+7)   (11+9)
(3+8)   (-2+11)
 
 
  =
 
12   20
11   9
 
 

Question 3:

Find the sum of the following matrices

A =
 
-1 2 3
5 8 -10
 
 
B =
 
1 5 7
-3 2 0
 

Solution:

A+B=
 
-1 2 3
5 8 -10
 
+
 
1 5 7
-3 2 0
 
 

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

                      
  =
 
(-1+1)   (2+5)   (3+7)
(5+(-3))   (8+2)   (-10+0)
 
 
  =
 
0   7   10
2   10   -10
 
 

Question 4:

Find the sum of the following matrices

A =
 
1 2 -1
5 6 3
8 9 -10
 
 
B =
 
-1 0 5
3 4 2
1 4 -3
 

Solution:

A+B=
 
1 2 -1
5 6 3
8 9 -10
 
+
 
-1 0 5
3 4 2
1 4 -3
 
 

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

                      
  =
 
(1+(-1))   (2+0)   (-1+5)
(5+3)   (6+4)   (3+2)
(8+1)   (9+4)   (-10+(-3))
 
 
  =
 
0   2   4
8   10   5
9   13   -13
 
 

Question 5:

Find the sum of the following matrices adding two matrices.

A =
 
-3 4
-8 5
5 6
 
 
B =
 
1 2
3 4
-5 3
 

Solution:

A+B=
 
-3 4
-8 5
5 6
 
+
 
1 2
3 4
-5 3
 
 

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

                      
  =
 
(1+(-3))   (2+4)
(3+(-8))   (4+5)
(-5+5)   (3+6)
 
 
  =
 
-2 6
-5 9
0 9
 
 

These are the problems in the topic

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Adding Two Matrices to Matrix Introduction