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: matriciesso whoever wrote it like mr. k you might want to change it.

 

AND SO THE NEXT SCRIBE IS CRIS