Matrices 2: Armageddon!!!! (multiplying)

Alright, I'm Nemo, Silvers partner in crime. We're are doing our blog project, for the SVRSS Gr. 12 Applied math program.


Okeey-Dokeey, Lets get started. Multiplying Matrices. This is different then Scalar Multiplying. Instead of multiplying each number inside the matrix by a set number, things are done a bit differently. Let me show you.
1.





2.

3.

4.

Alright, I'll be referring to the pictures in the next little bit, so I numbered them.

When you are first going to multiply a matrix, you must know whether the matrices can by multiplied together of not. Here is how you know,

"The Number of Rows in the second matrix must match the Number
of Columns in the first Matrix"

as told in image 1. Which means, If you have matrix [A](2x2) and matrix [B](4x2) you cannot multiply [A]x[B] Because the row in [B](4) doesn't match the column in [A](2). But you can multiply [B]x[A] Because the row in [A](2) matches the column in [B](2).

Now for the Second part of image 1.

"The dimensions of the Product matrix are : The # of Rows in the First
matrix X The # of Columns in the Second Matrix."

This means that when we multiply [B]x[A], the end product will equal 4x2.

All of what I just said is in a more visual form on image 2.

Now, the next little bit I'm going to tell you should be known, but you don't need it since your calculator does it for you. Mr. Maksymchuk recommends that you NEVER do it by hand, at least when you have a calculator to do it. But I will show how to do by hand anyways, just so you know how it works.

Referring to image 3, we are going to learn the Two finger rule. You multiply the first row of the first matrix, by the first column of the second matrix(a x e and b x g) You then add the products of those and add them together for the first number in our product matrix. For the second number move over to the second column in the second matrix. Then the second row in the first matrix and the first column in the second matrix, so on and so forth.

Image 4 is where all we have learned in image 3 comes into play, and is used. There is a screen shot as to prove that is done right.

Remember, we shouldn't have to use the two finger method if we have a calculator.

And that is how multiplying matrices by matrices work.

Thanks for your time

Nemo