Dimensions of A Matrix

You find the dimensions of a matrix by counting the rows and by counting the columns. The rows of a matrix goes from the left to the right, but the columns of a matrix goes up and down. The dimensions of a matrix is displayed as row by column.

1x3 Matrix

3x3 Matrix

 

3 x 2 matrix.

  3 x 3 matrix.

 

Error Analysis

1) 

It is wrong because they did not notice that the gragh was going up by 5 instead of 1.

Answer: y=2x+9

2) 

It is wrong because they should have tried to check it on both of the equations.

Answer: (1.1,-1.5)

3) 

22 is wrong because it should have a dotted line. Number 23 is wrong because it should be shaded above the line.

4)

20 is wrong because it should have a dotted line. Number 21 is wrong because it should be shaded below the line.

Graphing Absolute Values

The equation for absolute value equtions is y=a|x-h|+k.
The vertex of the graph of an absolute value equation will be (h,k).
The a in the equation tells you if the equation will open up or down.
If h is negative the vertex will move right by the number that h is, but if h is positive it will move left by the number that h is.

Systems of Equations

Independent and consistent system	Inconsistent system	Dependent system

:
Independent systems have one solution and
one intersection point.

Inconsistent systems have no solution and
no intersection point.

For dependent systems the solution is the
whole line.