BOB

Oops i almost forgot to write my BOB.

I think the Matrix unit is not really a hard one, but it is tricky. The part where i had problems was the transition matrix. It's kinda confusing at the beginning, but the grouping thing really helped even though I like working alone, much. That's all, good luck on the test !

February 16, 2007

During our Friday class Mr. K inroduced to us the smartboard, then we had a pre-test in the morning & we were group into 4 & compared each others answer in the group. Then in the afternoon class Mr. K gave us some problem to solve. Obviously Mr.K didn't gave us any new lesson so im just going to solve one problem from the h.w. review from the book pg.89 #5.


- A young entrepreneur decides he will sell tank tops, short-sleeved T-shirts, long-sleeved T-shirts, and sweatshirts. The table below shows the cost to produce each item.

a.

b.

c. Determine the total projected costs.
-> [T] [S.] =

-> then add those two #'s to get the total cost.
-> 10606.25+1850 = 12456.25
-> so the total cost is $12456.25


THE NEXT SCRIBE IS AL

gOoD lUcK gUys On tHe tEsT!.... :D

SmartBoard Notes

Here are the slides from this afternoon's class.

February 15, 2007

In today's class we just worked on another question about transition matrices. Mr. K did not teach us any new stuff today, so I am just going to answer one of our assignment from the other day.

page 83, #4

4.If Regan passes his math test, the probability that he will pass the next one is 97%. If he fails his math test, the probability that he will pass the next on is only 85%. Regan has worked hard on this unit so the probability that he will pass the first test is 95%.

a) Write the initial probability matrix and the transition matrix.

b) What is the probability that Regan will pass the fifth test.

[S] x [T]^5 = [.97 .03] (therefore Regan has a 97% on passing his fifth test and 3% on failing it)

I did not show my work because I know that you guys already know how to answer this kind of question.

We also talked about the up coming project on matrix. Mr. K just show us the different kind of presentation we can choose from. If you missed the class that day or you just want to know more about it, just visit our blog and read the post "PRESENTATIONS ......".

This is the end of my scribe.

The next scribe is Jowell

February 14, 2007

February 14, 2007

Hi everyone. Happy Valentines day. Today in the third period class we tried to do a question mr. k put on the board. my computer isn't working well so i can't put any pictures on or it will freeze.

In class we learned how to make equations out of the information given because we were supposed to make an equation out of a matrix.

ex. you have a matrix that is 3 by 3 and the info from left to right starting from the top, and it has these values,

f to f = .85, f to c = .13, f to e = .02 then the middle row has, c to f = .05, c to c = .91, c to e = .04, the the bottom row has, e to f = .03, e to c = .21, e to e = .76.

Then you have the initial state which was, f = .30, c = .20, e = .50.

So we had to make three equations out of this information.

ex. Make an equation out of the f column by mulitplying the f column by the initial state.

and it should look like this:

F= 0.85f + .05c + .03e.

and that would give you the new information for the f column.

Then to get the new info in column c, you have to do the samething as before but this time using the c column.

Then over again to do the e column.

In last period, we looked at a review for the matrices unit.

We were asked to do question 6 in the booklet.

Question from booklet:

Three children, Ann (A), Bill (B), and Carl (C) are throwing balls at each other. Ann always throws to Bill, Bill always throws to Carl, but Carl is equally likely to throw the ball to bill as he is to Ann. Write a probability matrix to represent this situation?

So we made a matrix with percents.

ex. matrix 3 by 3 had FROM A B C, TO A B C. In the A row we put 0, 1, 0. In the B row we put 0, 0, 1. In the C row we put 0.50, 0.50, 0.

The initial state had 1 0 0 starting with Ann.

And that was it but mr. k asked us to figure out the percentages for Ann, Bill, and Carl after the fourth throw.

So we used the initial state and multiplied it by the transitional matix to the exponent of 4 to get the percentages.

And we got: 0, 0.50, 0.50.

Meaning, if Ann started with the ball then she threw it to Bill, Bill then threw the ball to Carl, and then the ball ended up with Bill. The ball then had a 50-50 percent chance going to Carl and Bill again. So if you want to figure out the longterm percentages, you have to take the initial state and multiply it by the transitional matrix to the exponent of 50 and then you get Ann with a 20 percent chance to get the bal and Bill and Carl a 40 percent chance to get the ball.

So do you really think it's a fair game?

Also for people who were not in the afternoon class we had to tak these notes down in our dictionaries:

MATRIX:

A rectangular arrangement of numbers (or letters) in rows and columns contained in square brackets. The plural of MATRIX is MATRICES. They are usually named using capital letters.

ex. a 2 by 3 matrix: square bracket row (1 2 3) bottom row (4 5 6).

DIMENSIONS OF A MATRIX:

Determined by the number of rows and columns. Written as: r x c READ as "r by c"

ex. Matrix above is a 2 x 3 matrix.

ELEMENT OF A MATRIX A.K.A. ENTRY

One of the values in a matrix. The address of each value is given by its row and column position.

ex. A (sub) 23 = 6

The element in matrix , row 2, column 3 is 6.

We also had to finish the homework on p.83 numbers 6 to 9.

OH YEAH........mr. k kept om spelling matrices like this: matricies so whoever wrote it like mr. k you might want to change it.

AND SO THE NEXT SCRIBE IS CRIS

Matrices

Today's class was just basically a recap of last nights homework. The homework was confusing to a lot of us so here is one of the questions. I will try to see if i can give you a better understanding of this question based on what i learned.

1. If a train is late on one day, there is a 90% probability that the same train will be on time the next day, while if the train is on time, there is a 20% chance it will be late the next day. If in a given week it arrives on time on Monday, compute the probabilities that it will be on time or late for each of the subsequent days of the week. What would the corresponding probabilities have

been if the train had been late on Monday.

In this matricx (T) represents on time and (L) represents late. So as you can see the numbers stated in the problem have been inserted into matricx. Now because there is a .20 there has to be a .80 at the (T) (T) location. This is because each row must equal 100 or 1 depending if u are using whole numbers or percents. So following this rule there has to be a .10 at the (L) (L) location.

Now that we got the transition matricx we need what is called a state matricx. A state matricx is what happens first, because the train was on time on Monday the state matricx has to be;The (1) represents the on time colum and the (0) reprsents the late colum.

So to find the percentages of the train coming late or on time you would take the transition matricx and multiply it by the state martricx like this;

If u muiltpy these two matrices you will get the percents of the train being late or on time for the next day. If you multiply the result by the transition matricx you will get the percents for the third day and so on and so on ........

Now if the train happened to be late on that first Monday then the transition matricx would stay the same and the only difference with the state matricx is that the 1 and the 0 would be switched around.


Definitions:

Transition Matricx.....is the matricx showing how things change over time.

State Matricx.....is the matricx in which things begin

Another thing to remember is that if you are trying to find what the numbers stabilize at, rather then keep pressing enter on your calculator just rise the transition matricx to a high number and you will be able to see the numbers at which the amount stabilized. But remember this way only works if you are not interested in finding the exact time that the number stabilized.

I hope my scribe made it easier for you guys to understand things.

The next scribe is chris

BOB

My first reaction to matrix was that it was going to be an easy subject since it looked and sounded simple, but I was wrong. To be able to figure out these matrices, must know what your doing and focus on it since you wont get lost without knowing it. The way these matrices are added, subtracted or times, i mean "multiplied", is not like normal addition or subtraction. You must know which ones go together and you must also satisfiy the rows and columns. In the beginning i had trouble with this part, but as the participation of the class increased, i started to understand bit by bit. So it really goes to show that "Learning is a conversation"

Transition Matrix

In the beginning of todays class, we had a review on last weeks lesson about multiplying matrices. Transition matrix was then introduced to us. Transition matrices involves probabilities and percentages. It describes change and can be symbolized with "[T]" To be able to work with these matrix, the columns and rows must have the same information.

This example I'm about to give is from the first transition matrices worksheet Mr K handed out. We had a hard time understanding example 2, which was the sports one, so ill re-cap on that one..

EXAMPLE 2, SPORTS
The annual Oxford-Cambridge boat race, has been rowed regularly since 1839. Using the data from 1839 up to1982, there were 57 Oxford wins and 67 Cambridge wins. If the relationship between the results of a given year and the results of the previous year are considered, the following table can be constructed.



**



**-This means that Oxford got 35 games won after another (two games won in a row) and 22 wins without a two game in a row streak ... This goes the same for Cambridge.

To be able to work with this matrix, we need to convert to a percentage then to a decimal. I'm sure we all know how to convert these into decimals. the result should be.










Question: If Oxford wins this year, what is the probability they will win next year? in two years? in three three years?

Answer: to solve this question we need to have a transition matrix and a state matrix.

The transition matrix is :










This matrix represents the change. for example, there is a 61% chance that Oxford will have a two game winning streak.


The state matrix is simply stated "how it begins". For example, in the question it stated that Oxford won this year

Therefore we put a 1 under the column of Oxford in a 1x1 matrix which the rows represent the win. There is a zero under Cambridge because this represents the first year and they lost the first year.


We then multiply the transition matrix and the state matrix to get the probability of each team.
It goes:

2









The Transition matrix has an exponent of two which will give us the result for a second year percentage. We all know by now how to multiply matrices. That is the next step. the result is:











This means that in the next year. Both teams will have the same chance of winning between themselves.


.




.i hope this is much better than my other post.. :)

BOB; Ivy; Matrices

Well, this unit was fun and I think this is only the unit in Applied Math that I can understand because the rest it's pretty confusing but anyways. I think I can do okay on our Matrices Test; Hopefully. Matrices was pretty fun doing the code, the multiplication, adding, subtracting, connectivity, but the transition matrix I kind of get it I'm 80 percent sure...I just need more practices and understand each different method how to do it, whether population, weather, sports or diseases. It's just freaking me out when Mr. K was telling us in our class that we actually use a little bit of probability, because seriously "I NEED HELP UNDERSTANDING PROBABILITY AND STATISTICS" I'm pretty low of understanding when it gets to that, but hopefully my second time in AM40s will be better for me. Okay that's it.

Matrices

When Mr. K first introduced the unit Matrices I felt like I knew what was going on, this unit seemed like it was going to be easy and we would just breeze right on through but I was wrong. The next day we were introduced to matrix multiplication and to be honest I was so confused but as the class went on I began to understand more and more. The finger method really helped me to be able to do the multiplying part. I also liked that assignment on decoding the messages, that was pretty fun. So I think if we all just buckle down and help each other out we’ll all be fine.

BOB

When we started learning about Matrix Multiplication I think it was on Wednesday's third period class, I thought i was a little intimidating at frist. I was a little confused about how we were supposed to do it and what were the restrictions when doing it. But I think after doing some questions and doing the "fingering" method, i really got the hang of it. When we first learned about the addition and subraction in matrices, I thought it would be a breeze because there was less work and next to no restrictions, but I think that we've all got our work cut out for us in this particular area of the unit. One thing that I thought was cool so far in this unit, was the decoding and encoding. I think that it's the coolest things as of now, because it is a part of the unit and very educational and at the same time it's fun to decode and encode messages. I didn't know what exactly to blog on, so I sort of just jotted down a few thoughts. I hope someone else blogs as well, i'm really looking forward to hearing someone else's input on the unit so far. K, bye! - Grace

The Matrices Code

As promised, here is the assignment you have to complete for Monday's class ... and the secret message I have for you is encoded beneath it ... decode it and bring it in to class on Monday. ;-)



Your secret message ...

-6, -9, -8, 10, 23, -23, -8, -35, 75, 8, -8, 24, -23, 21, -51, 31, -26, 62, 4, -2, 10, -19, 8, -41, 31, -12, 75

Network Matrices

Today in class we talked about NETWORK MATRICES. These matrices are used in the real world. Whether it is cables between computers, wries between telephones, railway networks, airplane routes between major centers, there is always a connection between places and things.

Connections may be achieved by "one-hop", "two-hop", "three-hop", "four-hop", etc.
I'll use airplanes as an example.

A "one-hop" is a direct connection between the two cities.
ex: one airplane trip (one hop) from Atlanta to Boston
A "two-hop" is the 2 different ways from one city to another with 2 different airplanes.
ex: one airplane trip (one hop) from Atlanta to Boston then another airplane trip (2 hop) either back to Atlanta, or Charlotte.
A "three-hop" is the 3 different ways from one city to another with 3 different airplanes.
ex: one airplane trip (one hope) from Atlanta to Boston, then another airplane trip (2 hop) to Charlotte, then another airplane trip (3 hop) back to Atlanta.
And so on...



For example:




We can create a "connectivity matrix" showing the direct routes of the network on the left side of this page.

We can create a matrix that represents the connection between A, B, and C. In this matrix we will need 3 rows and 3 columns.






When there is one direct route, you place a "1" in any cell which indicates a direct connection between two places. For example there is one route from A to B, so a "1" could go into the cell that connects A to B. When there is an indirect route, you place a "0" in any cell which indicates no direct connection. In this case, there is no route from A to C, so therefore in the cell that connects A to C, you would place a "0"



The matrix for the image above should be:










We also learned how to indicate where there is a "2 hop" route between places. In our example, is there a 2 hop route between A and A? YES! Because you are able to take a plane to Boston, and take another plane back to Atlanta. So in a matrix that indicates "2 hops", you'd place a "1" showing that there is a "2 hop" route between A and A. In our case, there is no 2 hop route from A to B. Because there is a plane that takes you from A to B, but the next plane will take you somewhere else besides B. So you'd place a "0" in the cell connecting A and B for "2 hops"


The matrix indicating "2 hop" routes should look like this:












Whatever number a connectivity matrix is raised to, will tell you how many different routes there are.
For example, if the connectivity matrix is raised to the power of 2, the result of that would tell us the number of ways from one place to another with 2 airplanes.
If the connectivity matrix is raised to power of 3, the result of that would tell us the number of ways from one place to another with 3 airplanes. ETC.









And tomorrow's scribe is....... JHAY-AR!!

Feb. 6, 2007, Ivy's Scribe Post

Hello...Everybody... Ivy is here to be your class scribe for today (I just got off from work I'm sorry I will post my blog next time pretty on time).

Well, anyone who missed Applied Math 40S, Feb. 6, 2007. Here is your hope to know what happened.

Mr. K introduced us The Matrix unit, and read the following as I explain everything.

The definition of Matrix is an array of numbers or letters with dimensions, that can be organize to add, subtract and multiply. Also Matrix can't be add or subtract if they have different dimensions. We also name a Matrix by it's own rows and columns.

There are also two different type of Matrix; a Rectangular and a Square.

A Rectangular Matrix has a different rows and columns.
example. 3 x 4 or 3 x 2

A Square Matrix has the same dimensions.
example. 4 x 4 or 5 x 5

Mr. K also showed us an example of a Matrix. He also told us to look for patterns, Can you find one? Try to look for patterns before reading bellow.



The First Student saw the patterns of a Diagonal Zeros. It means in this type of Matrix it is counting by distance so Brandon cannot travel to Brandon, because it is in the same place no point of traveling.

The Second Student saw the mirror like of the matrix by triangular.

The Third Student saw in every city either row or columns it says the same thing.

Later on. Mr. K gave us another Matrix and compare the Matrix above and the Matrix below.




The difference of these two Matrices are:

- This is a Rectangular Matrix
- This Matrix has a 3 x 4 dimensions
- This Matrix has no Contex





- This is a Square Matrix
- This Matrix has a 5 x 5 dimensions
- This Matrix has a Contex




After comparing the two Matrices Mr. showed us this;

Later on...He challeged us to look for these elements in the following Matrices above. Try it!



Hint. To find an element. Look at the picture.

The answers are:

Plus he got another challenges: To add and Subtract it.



Yet he got another challege.

Hint. if you see a scalar always multiply that number to the matrix beside it.


Ok...That's it for Feb. 6, 2007 class. The scribe for tomorrow is Kristel.

Multiplying Matricies

In mathematics, a matrix (pl. matricies) is a rectangular table of numbers, generally a table consisting quatities that can be added and multiplied. In today's class, we learned about the 2 kinds of multiplication in matricies. These 2 kinds are:

• Scalar Multiplication - is multiplying a matrix by a number.

Given a matrix A and a number n (which is 2), the scalar multiplication cA is computed by multiplying the scalar c by every element of A.

For example:

A

• Matrix Multiplication - is the multiplication of two matricies where the number of columns of the left matrix is the same as the number of rows of the right matrix. This involves both multiplication and addition.

For example:

2 x 3 2 x 2 2 x 2

A B C

If A is 2 x 3 matrix and B is a 2 x 2 matrix, then the resultant matrix C is a 2 x 2 matrix. Why? Look at the dimensions of the 3 matricies. The inner dimensions are the number of rows and columns of matrix A and the outer dimensions, as we can see, are the dimensions of the resultant matrix C. Is this example commutative? Yes, because in this example, the outer dimensions are the same, which means we can multiply the matricies. In our examples in class, the inner dimensions of the matricies should be the same to multiply them.

And the next scribe is... Jennifer

Matrices Homework Assignment 2

As promised, here is is. Your assignment is to do questions number 1 through number 6. Click on each image to enlarge.

I will most likely hand out textbooks next week. By then all student timetables should be finalized and our class registration should be stable.

Matrices Homework

As promised, here is is. Your assignment is to do questions number 2 through number 8. Click on each image to enlarge.