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

Here's Matricies For Ya

Hi, I'm Silver, nice to meet you. I hope you are all well.

I am working with Nemo, to help teach you about matrices. As this is the first time this is being done (our schools doing this blog) I hope it works well, and does help our classes.

I am going to try to teach you how to ADD, SUBTRACT, and SCALAR MULTIPLY matrices, by telling you the rules and conditions that must be followed to either add, subtract or multiply the matrices. I will also give you examples that was given to my class to help explain what I am trying to tell you.

Now, I will start with ADDING the matrices.

To Add matrices they must have the same dimensions, meaning they must have the same amount of rows and columns.

This page that was given to my class by Mr.Maksymchuck just means what I said.... with a break-out of colors.

To simplify this color explosion, it tells us, if we look at matrix A and matrix B, that "0" can be added to "4", "1" can be added to "5", "2" can be added to"6", and "3" can be added to"7".

The result of which will be matrix C that would be:

[4 6]
[8 10]

As another example:

A [2x4] matrix can be added to another [2x4] matrix.

However, a [2x5] matrix cannot be added to a [3x6]matrix.

Now that I tried to explain ADDING matrices, I will now try to explain how to SUBTRACT them.

Subtracting matrices should be easily understood, so long as you know how to ADD matrices. I say it is easy because it follows the same rule, or the same condition as ADDING. "The dimensions must be the same."

For example:

A [5x5] matrix can be SUBTRACTED by another [5x5] matrix, exactly like matrices with these dimensions can be ADDED.

Next up is MULTIPLYING matrices. Now there are two kinds of multiplying, but I will teach you about one kind, SCALAR MULTIPLYING.

With SCALAR MULTIPLYING the whole matrix is multiplied by the SCALAR NUMBER.

This burst of color just explains that any matrix be it a [1x1], [2x10], or even bigger (any sized) matrix can be multiplied by any size of a scalar number.

The definition says that it is just a number, or just a value, that it doesn't give a direction.

today was a work period. See Edline for the solutions to the review given in class. Test is tomorrow. Matrices project due next Wednesday.

blog thing

today we learned about solving transition problems using matrices
the formula is Pn=Po x Tn
Po is the initial probability matrix and must be a row ex: [.5 .5]
to calculate probabilities for subsequent matrices we need to create a transition matrix
T is the transition matrix and must be a square ex: [.64 .35
.3 .7 ]
the numbers must be in decimal format cuz your dealing with percentages
we had to work on page 83 in the book # 1-9 but not 2
test on Friday

Today was a work period. We worked on old exam questions.

Richard needs some school supplies. In the following matrix, he compares the cost ($)
per package for the same three items from three different stores. These costs do not
include taxes.
store X store Y store Z
pencils 1.59 1.89 1.69
A= pens 1.79 1.49 1.99
notebooks 2.09 1.69 1.79

a) Calculate the cost per package including taxes. Show your work using matrix
operations. (GST = 6%, PST = 7%)

A x 1.13= 1.80 2.14 1.91
2.02 1.68 2.29
2.36 1.91 2.02

b) If Richard needs 2 packages of pencils, 1 package of pens, and 5 packages of
notebooks, at which store should he shop to get the lowest price? Show your work
using matrix operations.

1.80 2.14 1.91 storeX storeY storeZ
[2 1 5] x 2.02 1.68 2.29 = [17.42 15.51 16.22]
2.36 1.91 2.02

He should shop at store Y.

here's the link if you want:
http://www.edu.gov.mb.ca/k12/assess/archives/ap_mg_june_08.pdf

Today we learned how to solve route matrices. We had a work period to do questions 1-6 on page 76 in our textbook. some important things to remember is that A means 0 stopovers, A squared means 1 stopover, A cubed means 2 stopovers and so on. A + A squared = 0-1 stopovers, A + A cubed means 0-2 stopovers. Some examples of route matrices would be the different routes you could take from Toronto to Vancouver via plane, or who can contact who in a spy network.

February 19th Math Blog*

Hello...
Today at the DRCSS we did Tutorial 2.2- Multiplying Matrices..
When multiplying a Matrice, multiply the first number in the row by the first number in the column.. then multiply the second number in the row by the second number in the column.. and so on then add the products.

** Two matrices, A & B, can be multiplied to form A X B only if:

• The Number of columns in A = The number if rows in B

If this is so. then the product matrix AB will have the same number of rows as A & the same number of columns as B.
Example: Amxn X Bnxp = ABmxp
--->> m,m are dimentions of product matrix.
--->> n,n must be equal.
*When you multiply matrices, AxB doesn't necessarily equal BxA

For today's assignment we had done questions 1,2,3,4, and your choice of either 5 or 6, on Page 64.

Hey everybody, how ya'll doin?! It's Courtney here and today is February 18 and it is chilly outside, about -20 without the wind blowing. Sure beats -50 though right! Are the roads still pretty icey out there? Not going to lie, I was scared to even get into a vehicle for a while there.
We had fun in math class today learning about our new unit on tutorial 2.1 Matrix Operations on page 52 in our handy dandy applied 12 textbook!
A matrix is a rectangular array of numbers, known as the elements of the matrix. The array is enclosed within square brackets. Each element is a scalar in this unit.
The brackets are very important, so do not forget to put them in! Also, the row number always comes before the column number. This unit is mainly done on the graphic calculator, so it is probably a good idea to get out there and get one and remember to get four triple A batteries!
Mr.Bennet assigned homework on page 55 numbers 1,3,4,5,7,8! Holy Macaroni, you better get started you guys!
Well my time on here has come to an end, but I can promise you I will be back! Nice meeting you :)

Keep it real,
Courtney

Getting To Know You....(isn't that a famous song by someone my parent's age?)

What's the weather like in Dauphin? How about the highways? Buses run today? Consider this a shout out trying to discuss things other than Probability / Matrix Modelling.....The way I see it, we should 'break the ice', somehow, although in light of recent weather phenomena, maybe it's best to just say hello to each other....

So, Hello!

RM

February 11, 2009 D.R.C.S.S

Today at the D.R.C.S.S we did tutorial 1.4 on probability in our text books. We also learner about Independent and Dependent events.

Example: What is the probability that a coin will land heads in each of 4 consecutive tosses?
P(4 heads in a row) = 1/2 x 1/2 x 1/2 x 1/2

= 1/16
The probability of tossing 4 heads is 1/16.

What I Think I'm Supposed To Have Learned...or Mentoring 101

At the end of our section on Matrix Modelling, I am confident (no, really, I AM confident), that my students here in Swan River will be more than capable of teaching their peers in Dauphin some of the finer points regarding what we've covered so far.

Specifically, what they'll be doing (or what you'll be doing, if you happen to be unfortunate enough to have landed on my class list this semester), is this:

photo credit: http://www.svleck.com/images/helping%20students%20stat.png

1. In your Blog Team, begin a series of posts describing the 'ins and outs' of one sub-topic in the unit on Matrix Modelling. I'll tell you in class who your team is, and what your sub-topics are.

2. Your language is critical to the success of such an experiment. You need to talk on the blog like a high school student speaking with another high school student (whom you don't know), since that is exactly the situation that we're in. Grammar, spelling, and punctuation are really important, since you don't know whom you're speaking to, and the only thing that they have to base the quality of your instruction on is your language....Having said that, I think a sense of humour is really worthwhile, as is the sense that the world is much larger than our small piece of geography in the Parkland...

3. I hope that it's obvious that I expect you to post screen shots, recordings, external links, etc....including anything and everything that might help the students in Dauphin learn what you're supposed to know...Be creative, and think carefully about what you're posting...

Rationale: Am I expecting my students to 'create' learning opportunities for other students in other communities, just because? Believe it or not, I'm not really that crazy about 'busy work'....Teachers as well as students are busy, and need to trust that their time is well spent in learning environments/opportunities....So here's my take...(and I take absolutely no credit for this idea, it's just 'common' knowledge, especially to first-year teachers)....

"Having to teach something to someone else
makes you learn it yourself, really, really, well...."

....which I hope does a quick job of explaining at least one of the reasons why we're doing what we're doing....

RM

Tutorial 1-3 slides

video (zipped)

Tutorial 1-3

And another chapter begins...

So Mr. Bennet and I have schemed a bit to 'open up our world' a little with respect to the idea that our students need to be exposed to some different things with regard to online learning.



We thought (actually, it was mostly Mr. Bennet's idea, but I'll happily agree with ideas that aren't mine and that I believe are worthwhile....) that we would create a blog populated by authors from each of our respective classes in Grade 12 Applied Math. So here we are.



Yes, this is new....



Yes, this is a little experimental....






photo credit: www.fotosearch.com/comstock/oddballs/CSK161/


No, we've never done this before...



No, we're not really sure how it's exactly going to turn out...



I am, personally, by nature, at least somewhat optimistic generally about new things. I'm excited about learning from and with new people, and I believe as a teacher that I owe it to my students to explore and learn with them. Let's keep our minds open, and let's keep track of the things we do well to share with others, and also the things we need to improve upon to help future students and teachers embarking on similar journeys....



Here in my school, our semester starts tomorrow, so I'll meet my students then....



Any thoughts, Mr. Bennet???



(or comments?)