[Tutorial][Python] Multiplying a Matrix by Another Matrix

Suppose there are 2 matrix for multiplication: This is the most basic method to do matrix calculation. In example shown below, 2 is so called scalar in this calculation. We multiply each number in matrix by this scalar 2, and mark multiplied result in same location in matrix.

*The number of columns in A need to equal to the number of rows in B.
To calculate that we need to do an action named “dot product”
 

 With python, we can use .dot() to calculate the dot product for these 2 matrix:



Example for Multiplying a Matrix by Another Matrix

Question 1) 

4*1+5*0 = 4+0 = 4
Result is 4

Python :

import numpy as np
from scipy import linalg

A = np.array([4,5])
B = np.array([[1],[0]])
print(A.dot(B))

Result:

[4]

Question 2

From a to f in order, there are the calculation order with use dot product :

a: (1,-2) • (4,-1)  = (1*4)+(-2*-1)  = 4+2 = 6
b: (0,3) • (4,-1)  = (0*4)+(3*-1)   = 0-3 = -3
c: (-1,4) • (4,-1) = (-1*4)+(4*-1)  = -4-4 = -8
d: (1,3) • (1,2)   = (1*4)+(-2*-1)  = 1-4 = -3
e: (0,3) • (1,2)   = (0*4)+(3*-1)   = 0+6 = 6
f: (-1,4) • (1,2)  = (-1*4)+(4*-1)  = -1+8 = 7

Calculation with Python:

import numpy as np
from scipy import linalg

A = np.array([[1,-2],[0,3],[-1,4]])
B = np.array([[4,1],[-1,2]])
print(A.dot(B))

Result :

[4]

Reference:
http://chortle.ccsu.edu/vectorlessons/vmch15/vmch15_4.html


Question 3
This is a question from Math is fun website:
https://www.mathsisfun.com/algebra/matrix-multiplying.html

From information, i create 2 matrix:

And the result would be in this format: [a,b,c,d]

a.        (3,4,2) • (13,8,6)   = (3*13)+(4*8)+(2*6)  = 39+32+12 = 83
b.        (3,4,2) • (9,7,4)     = (3*9)+(4*7)+(2*4)    = 27+28+8   = 63
c.        (3,4,2) • (7,4,0)     = (3*7)+(4*4)+(2*0)    = 21+16+0   = 22
d.        (3,4,2) • (15,6,3)   = (3*15)+(4*6)+(2*3)  = 45+24+6   = 75

Result is [$83,$63,$22,$75], which’s means
A.        Sold are monday are $83.
B.        Sold are Tuesday are $63.
C.        Sold are Wedenday are $22.
D.        Sold are Thurday are $75.

Calculation with Python:

import numpy as np
from scipy import linalg

A = np.array([3,4,2])
B = np.array([[13,9,7,15],[8,7,4,6],[6,4,0,3]])
print(A.dot(B))

Result

[83 63 37 75]

Reference:
http://chortle.ccsu.edu/vectorlessons/vmch15/vmch15_4.html
https://www.mathsisfun.com/algebra/matrix-multiplying.html