SOLUTION: compute the matrix product AB for: A = [2 3 0 -4 2 1 3 0 -2] B = [-1 2 3 3 0 -2 0 4 0]

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Question 441330: compute the matrix product AB for:
A =
[2 3 0
-4 2 1
3 0 -2]

B =
[-1 2 3
3 0 -2
0 4 0]
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Rule for multiplying two 3x3 matrices:



So, using the above rule:

 

                                  
Edwin

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I don't recommend using and/or memorizing the formula the tutor Edwin mentioned.

Instead it is better to highlight the first row of matrix A and first column of matrix B.

We'll align the terms like so
row1 of A:230
column1 of B:-130


Multiply straight down (eg: 2*(-1) = -2)
row1 of A:230
column1 of B:-130
Product:-290

Then add up the products to get -2+9+0 = 7

This result of 7 is the entry in the answer matrix that is in the first row and first column.

The answer is of the format %28matrix%283%2C3%2C7%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29

Follow this thought process for the other entries.

For instance, the 2nd row and 3rd column of the answer will involve row2 of A and column3 of B.
Let me know if you have further questions.

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Here's a similar example

Image Source:
https://towardsdatascience.com/a-complete-beginners-guide-to-matrix-multiplication-for-data-science-with-python-numpy-9274ecfc1dc6


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Another example

Image Source
https://www.mathsisfun.com/algebra/matrix-multiplying.html
The scratch work highlighted in yellow would be something like this
1*8 + 2*10 + 3*12 = 8 + 20 + 36 = 64