Wednesday, February 6, 2008

Multiplication by a Scalar

Hello everyone. Today in class we talked about:

+ Adding and subtracting matrices
+ Multiplication by a scalar
+ How to solve matrices on your calculator (TI-83 Plus).

For the first 10-20 minutes of the class we reviewed the concept of adding and subtracting matrices, followed by some review questions.

Multiplication by Scalar
We took up some vocabulary:

Vector: is a number that has a magnitude and a direction.

Scalar: is a number that has magnitude but no direction

Before class ended we took up a question about multiplying by a scalar:

NOTE: I used the ( ` ) to help space my test

``[ -3````` -15`````-13 ]
8 [ -20`````13````````4] = ? How do you find the answer?
``[ -12``````-6````````5 ]


Simple...


To find the answer you just need multiply the scalar which is the number 8, and multiply it on every number in the matrix. It should be something like this...

``[ -3``` -15```` -13 ]`````````````````````[ 8 x -3````` 8 x -15````` 8 x -13 ]
8 [ -20`` 13`````` 4 ] `````````=````````` [ 8 x -20```` 8 x 13```````` 8 x 4 ]
``[ -12`` -6 ```````5 ] `````````````````````[ 8 x -12```` 8 x -6````````` 8 x 5 ]


The Answer is....

``[ -3``` ``-15```` -13 ]```````````````` [ 8 x -3```````` 8 x -15 ``````````8 x -13 ]
8 [ -20 ```13 ```````4 ] ```````=``````` [ 8 x -20 ```````8 x 13````````````` 8 x 4 ]
``[ -12```` -6```````` 5 ]```````````````` [ 8 x -12```````` 8 x -6````````````` 8 x 5 ]

`````````````````````````````````````````````[ -24``````` -120```````` -104 ]
````````````````````````````````` = `````````[ -160``````` 104`````````` 32 ]
`````````````````````````````````````````````[ -96````````` -48 ```````````40 ]

NOTE: I used the ( ` ) to get proper spacing in because it seems like only adding spaces doesn't work.

Solving Matrices with a Calculator (TI-83 Plus)

Example:`````````````
-11[``13``]

To solve this on your calculator you must follow these simple steps:

  1. Turn on the calculator
  2. Hit the yellow key (2nd)
  3. Now hit the key below the MATH key, (x-1)
  4. You are now in the MATRIX program of your calculator
  5. Now hit the arrow key twice to the right, which puts the selector on EDIT
  6. Hit ENTER
  7. There on the top of the screen should now say, MATRIX[A] followed by a number X number. For our example we only have 1 row and 1 column. So press 1 ENTER 1 ENTER
  8. Now type in the number you see in the matrix. In our example it is 13. So press 1 3 then ENTER
  9. Now to get back to the main screen, press the yellow button (2nd) followed by the MODE button.
  10. Now type in the scalar of the problem. For our example it is, 11. So type in 11 in your calculator.
  11. Now to apply the Matrix, you must repeat steps 2 and 3
  12. You are now back in the MATRIX program, now press ENTER. After pressing ENTER you should have returned to the main screen of your calculator with 11[A] on your screen.
  13. Now press ENTER. You should have come up with an answer that is [ 143 ]. You have successfully answered the example question.
  14. Now, pat yourself on the back for a job well-done

This is the conclusion of today's class. If you are confused or have found any mistakes in this topic, please feel free to leave a comment.

The next scribe is..... charmel

6 comments:

Chunky said...

btw this is Adamson aka Chunky. I hope this helps with the homework

Lani said...

Hi Chunky,

Thanks for the good directions that you have included.

You noticed that adding spaces with the space bar doesn't work. If you use these six characters keyed just this way   (which is ampersand, n, b,s,p ;) it will create one space for each time you key them together.

Hope this is helpful,
Lani

elaineee said...

hey guys, im still not quite sure about this whole blog thing. but i was wondering if you guys had understood the first three questions of the homework assigned today. is there anyone that can help me with it?

d[x_x]b said...

im having difficulties with the first 3 questions also.

Chunky said...

same here -_-"

Chunky said...

btw thanks for the tip Lani