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]

Algebra.Com
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)   (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)   (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

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.

--------------------------

Here's a similar example

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


-----------------------

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
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