Matrice multiplication

When you want to multiply matrices you have to do row*column and sum the products!
You will repeat this several times:

Chapter 2: Dimensions of a matrix

The number of rows and columns in a matrix are written in the form rows×columns.

If you have a matrix like this   __    __     
                                            / 1 2 3 /
                                            / 4 5 6 /
                                            / 7 8 9 /

it has 3 rows and 3 columns, so the dimensions are 3×3. You read it aloud " three by three"
Matrices like that are called "square matrix"

Always remember: rows×columns       

 This is is a 1×3 matrix                            

This is a 3×3 matrix

This is a 3×2 matrix

This is also a 3×3 matrix (square matrix!)

The Identity Matrix

This is an example for an identity matrix.

Error Analysis

Mistake1:  The mistake is that "x" is going up by 5 and not by 1. The slope would be 10/5. This equals 2 and not 10/1!

Mistake2: The mistake is that he only checked 1 equation, but he had to check both!

Mistake3:  The mistake of the first graph is that it is a solid line and not a dotted line!
The mistake of the second graph is that it is shaded below and not above!

Mistake4:
The mistake in the first graph is the solid line. It should be a dotted line.
The mistake in the second graph is that it is shaded above. It should be below.

Graphing y=a/x-h/+k (Absolute Value Functions)

When you want to graph a equations like y=a/x-h/+k you have to follow this rules:

1. The vertex on your graph will be (H,K)  

2. a tells you wether the V is opened up or down
    If its negative its opened down, if its positive its opened up


3. the h moves the V to the right or to  the left
    If the h is positive it moves to the left, if its negative it moves to the right


4. k moves the V up or down


This is how it looks like

If y is greater you shade above, when its less you have to shade below and use a dotted line!