So you want to learn (or practice) manual matrix multiplication.
When you first start out with that topic, it is easy to make little errors that are hard to retrace
or to be confused by the methology.
This little tool walks you through an example and then lets you practice until you can multiply matrices in
your sleep. And it is actually fun!
Hint: This is also great practice for mental arithmetic.
This mentor assumes some foundational knowledge about matrices, for example what they are and why you would want to maybe multiply them. There are a lot of great introductory articles, for example here and here. If you are ready, get the first pair of matrices:
Multiplying matrices is very easy once you got it. First, we match each row of the first matrix with each column of the second matrix. That sounds weird, but there is a great trick that you can replicate on paper as well. Click the button below to see how it works!
For each field of our future result matrix, we will get the dot product of the row and the column "pointing"
to it.
That simply means to multiply the corresponding values (as in: the first value of the row times the first
value of the row, the second times the second, and so on) and add them all up.
This step is the hardest one to put in words, which is why we put it in colors.
Multiply the two blue values and the two orange values
and add the two results together. Write the result into the highlighted
field:
Good work! Do the same for all the three remaining fields now.
You got the basics down. You can now practice and build skill with as many exercises as you want. They get harder over time, so keep at it!