Multiplication of Two Matrices





In this page multiplication of two matrices we are going to see quiz on multiplying two matrices.

Multiplication of two matrices:

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

Question 1:

Multiply the following matrices

A =
 
1 3
7 4
 
 
B =
 
-3 1
8 -7
 

Solution:

AB=
 
1 3
7 4
 
x
 
-3 1
8 -7
 
 

Here we have two rows and two columns each row must be multiplied with every column of the second matrix.



=
 
1 3
 
x
 
-3
8
 
 
 
1 3
 
x
 
1
-7
 


  
 
7 4
 
x
 
-3
8
 
 
 
7 4
 
x
 
1
-7
 

=
 
(-3+24) (1-21)
(-21+32) (7-28)
 

=
 
21 -19
11 -21
 

Question 2:

Multiply the following matrices

A =
 
5 11
3 -2
 
 
B =
 
7 9
8 7
 

Solution:

AB=
 
5 11
3 -2
 
x
 
7 9
8 7
 
 

Here we have two rows and two columns each row must be multiplied with every column of the second matrix.



=
 
5 11
 
x
 
7
8
 
 
 
5 11
 
x
 
9
7
 


  
 
3 -2
 
x
 
7
8
 
 
 
3 -2
 
x
 
9
7
 

=
 
(35+88) (45+77)
(21-16) (27-14)
 

=
 
123 122
5 13
 

Question 3:

Multiply the following matrices

A =
 
-1 3
0 5
 
 
B =
 
1 2
-3 7
 

Solution:

AB=
 
-1 3
0 5
 
x
 
1 2
-3 7
 
 

Here we have two rows and two columns each row must be multiplied with every column of the second matrix.



=
 
-1 3
 
x
 
1
-3
 
 
 
-1 3
 
x
 
2
7
 


  
 
0 5
 
x
 
1
-3
 
 
 
0 5
 
x
 
2
7
 

=
 
(-1-9) (-2+21)
(0-15) (0+35)
 

=
 
-10 19
-15 35
 





Multiplication of Two Matrices to Matrix Introduction