discrete_matrices

Matricides MATRICES

BY: Brendan, Gloria, Essence, Darrius

3rd Period

May/20/2008

What is a Matrix?

A matrix, is very simply, an assortment of items arranged into a table. (The table is made up of Rows and Columns) For example a 3x3 matrix would have dimensions of 3 rows by 3 columns. Each ‘value’ or data is called an element.

This chart to the Left represents a 3x3 matrix

(3x3 meaning 3 columns by 3 Rows)

Why should I care about matrices?

Perhaps you’ve used a spread sheet in order to arrange your finances/taxes. Or if not for finances, any kind of data. Rather than list out all the data on many pieces of paper, you can use a matrix to neatly organize/categorize them in a single chart.

On this chart to the left, you can see a blank spread sheet. This can be useful for arranging data.

Can I add matrices?

Lets say we have two matrices. Both have dimensions of 3x3. How would we add them together? Well, first both matrices must be compatible. This means that the number of rows and columns must be the same in both matrices. The answer will

also follow this pattern.

Example below:

Note the color coding examples

2 4 6

8 10 12

14 16 18

Is the resulting Matrix.

Note how the Dimensions stay as 3x3

Now how did I do that? Simply By adding straight across the

matrices.

1+1=2 which becomes the 1st slot

2+2=4 which is the 2nd slot, and so on.

On the previous page, note how I Color coded the numbers that

add together

If I can add, then I must be able to subtract!

Subtracting can also be done in the same fashion as adding.

However instead of adding, you subtract, Straight across, as in the

previous example.

(Obviously we subtract the elements, because we are doing a

subtraction problem)

Example can be provided on board, if requested

Then that means… I can multiply matrices too!

Yes… however, this is one condition!

In order to multiply two matrices together, the number of columns in the first

matrix, must contain the same number of elements as the rows of the second

matrix.

So.

1) 2x2 matrix multiplied by a 2x3 matrix

These can be multiplied together, because the first matrix contains 2 columns, and

the second matrix contains 2 rows.

The resulting matrix, will have the dimensions of the “Outside numbers,

highlighted in blue”

So the resulting matrix will have dimensions of 2x3

(Example provided on board)

Determinant

How does one do a determinant problem? This is real easy stuff.

Simply grab a calculator, and make a matrix (what ever dimensions)

Then type

2nd, math, scroll over to MATH and pick

Det (

“Det(‘ should appear on your screen, simply put the matrix you made into the brackets and close it off with a

bracket.

Det([A])

Is what should be on your screen.

Inverses!

All you need to know regarding inverses, is that

To find the inverse, the equation is as follows.

A x A^-1=I

In order to do this on the calculator

Make a matrix, select the matrix, then hit the

X^-1 button

You should have something that looks like this

[a]^-1

Identity Matrix

1 0 0

0 1 0

0 0 1

This is an Identity matrix3x3

Example #1

E=[ 7 0] F=[5 -1]

[3 -1] [7 6]

[-3 4] [-2 0]

E+F=_______

Answer: [12 -1]

[10 5]

[-10 8]

Example #2

2F-3E

2[5 -1] - 3[7 0]

[7 6] [3 -1]

[-2 0] [-3 4]

Answer: [-11 -2]

[5 15]

[5 12]

Example #3

-5G

-5[4 2]

[6 1]

Answer: [-20 10]

[-30 -51]

Example #4

3F

3[5 -1]

[7 6]

[-2 0]

Answer: [15 -3]

[21 18]

[-6 0]

Example #5

2(E +F)

2([7 0] + [5 -1])

[3 -1] [7 6]

[-3 4] [-2 0]

Answer:[24 -21]

[20 10]

[-10 8]

Example #6

GH

[4 -2] * [-1 4]

[6 1] [6 2]

Answer: [8 4]

[36 2]