Muliplying Matrices

Before you can begin to multiply matrices you need determine whether or not the matrices can be multiplied. To do that you must write a dimension statement.

[3 4] [1 2 3]
[5 6] [4 5 6]
[7 8]
The dimension statement for this would be 3X2 times 2X3.

• The numbers on the inside (in red) must be the same to carryout the multiplication process
• The numbers on the outside (in blue) tell what the dimension of the solution will be. In this particular problem, the solution will be a 3 X 3 matrix.

If the two matrices can be multiplied, you then multiply row X  column and add the sum of the products to get the solution to the problem.

Dimensions of a Matrix

• When counting matrices, you must count row X column.
• If a matrix has the same amount of rows as it does columns, then it is a square matrix/
• If a matrix has zeros with ones going down diagonally, it is an identity matrix.

This matrix has one row and three columns. Its dimensions are 1 X 3.

This matrix has three rows and two columns. Its dimensions are 3 X 2.

This matrix has three rows and three columns. It is a square matrix and also an identity matrix. Its dimensions are 3 X 3.

This matrix has three rows and three columns. It is a square matrix. Its dimensions are 3 X 3.

• For this particular problem the value of x is going up by 5, so the slope should be 10/5 or 2 and not 10/1. By inserting the points, the final equation should be solved. With this answer, y is not equal to 9+10x in the t-chart.

• In order for a particular point to be the solution to a system, it has to solve both equations. So in this case (1,-2) solves the first equation, but not the second equation of the system.

• For problem #22 the shading is correct, but the line should be a dotted line, not a soild line. For problem #23 the solid line is correct, but the shading should be above the line, not below it.

• For problem #20 the shading is correct, but the line should be a dotted line and not a solid line. For problem #21 the sloid line is correct, but the shading should be below the line, not above it.

Graphing Absolute Value Equations

• The formula for graphing absolute value equations is y=a|x-h+k|. The point (h,k) is the vertex, point a determines how high or low on the y-axis the sytem will be, and point k also determines how far left or right on the x-axis the system will be.
• Point k: One thing to know about moving the system to the left or the right is that if point k is negative then you move to right. If point k is positive then you move to the left. The reason for this is because "standard form" is negative, which in turn makes +h negative.
• Point a: If point a is positive then the system moves up and if point a is negative, it moves down.
• If the equation has a slope of 1 and starts on point (0,0), it can be written simply as y=|x|.
• The higher the slope of the equation, the smaller the width of the system is.
• If the slope is a fraction, then the width of the system increases.