Matrix multiplication:
- So we will take two [2x2] matrices A= | 1 2 | and B= | 3 4 |
| 3 4 | | 5 6 |
-Firstly, A= | 1 2 | and B= | 3 4 |
| 3 4 | | 5 6 |
Take first row of Matrix A and first column of matrix B , now do this :
X1 = A(1,1)*B(1,1)+A(1,2)*B(2,1)
X1= 1*3 + 2*5 = 3+ 10 = 13
-Now, A= | 1 2 | and B= | 3 4 |
| 3 4 | | 5 6 |
Take first row of Matrix A and second column of matrix B , now do this :
X2 = A(1,1)*B(1,2)+A(1,2)*B(2,2)
X2 = 1*4 + 2*6 = 4+ 12 = 16
-After that, A= | 1 2 | and B= | 3 4 |
| 3 4 | | 5 6 |
Take second row of Matrix A and first column of matrix B , now do this :
X3 = A(2,1)*B(1,1)+A(2,2)*B(2,1)
X3 = 3*3 + 4*5 = 9 + 20 = 29
-Lastly , A= | 1 2 | and B= | 3 4 |
| 3 4 | | 5 6 |
Take first row of Matrix A and second column of matrix B , now do this :
X4 = A(2,1)*B(1,2)+A(2,2)*B(2,2)
X4 = 3*4 + 4*6 = 12+ 24 = 36
Now, we got 4 values X1, X2, X3 and X4
Thus, A*B =| X1 X2|
| X3 X4|
i.e A*B =| 13 16|
| 29 36|
For 3x3 matrix concept is same but the calculation becomes a bit long , so I am mentioning the formula or general syntax on how to multiply two 3x3 matrices.
Now, as you all have learned how we can multiply 2 matrices , let them be of any size.
We cannot multiply ever matrix as order[m*n] plays a very important role in multiplication of matrices.
Lets take 2 matrices A(m x n) and B (q x r)
Rule 1:
A x B is not necessarily equal to B x A. Order of multiplication can change our answers
Rule 2:
We can perform matrix multiplication only when:
-> n = q [ For AxB multiplication]
or
- > r = m [For BxA multiplication]
Rule 3:
The final matrix obtained my multiplication should have order
- > [ m x r ] for A x B
or
- > [q x n] for B x A.
That is it, for multiplication part.
Other concepts would be covered in next tutorials.
Bye Bye..
Comments
Post a Comment