# Warm-Up - PowerPoint PPT Presentation

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Warm-Up. Solve the following system of equations:. Reduced Row Echelon Form (RREF). Learning Targets. Possible solutions for a system The differences between RREF and Inverse Multiplication Using Reduced Row Echelon Form to solve systems. Quick Recap.

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Warm-Up

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### Warm-Up

• Solve the following system of equations:

## Reduced Row Echelon Form (RREF)

### Learning Targets

• Possible solutions for a system

• The differences between RREF and Inverse Multiplication

• Using Reduced Row Echelon Form to solve systems

### Quick Recap

• In order to setup a matrix our data must be:

• Setup in the Standard Form

• All similar variables must be in the same order

• Any missing variables in the equations must be represented with a zero

• Our matrix system using inverse multiplication has three matrices:

• Coefficient, Variable and Constant

### Recap Cont.

• Matrices cannot divide one another

• Multiplying the coefficient matrix by its inverse isolates the variable matrix

• Multiplying the constant matrix by our inverse as well will solve for the variables

### How many types of solutions can we have?

• Pause and Ponder, SILENTLY!

• One Solution

• No Solution

• Infinite Solutions

### Example

Solve using Inverse Multiplication:

What Does it Mean?!?

### Example

Solve using Inverse Multiplication:

AGAIN!?!

### Problems with Inverse Multiplication

• Inverse multiplication only produces a solution when there is only one solution.

• If we have no solution or infinite solutions then we will get an ERROR

• So how do we know if it is infinite solutions or no solution?

### RREF

• Reduced Row Echelon Form

• This form allows us to consolidate the coefficient and constant matrices into one matrix

• We can then perform row operations that will clearly state the exact answer

Old Way:

Coefficient

Variable

Constant

### How to set it up:

***Notice there is

no more variable

matrix and we add

the constant as an

additional column.

RREF

Coefficient

Constant

### Now to perform the math…

• In our calculators we can go under the matrix screen and select RREF

• We can then choose the matrix to perform this operation on.

### Solution

• The solution will be in a matrix that is the same dimensions.

• We can then read the results as variables and their solutions.

X-Variable

Y-Variable

Z-Variable

### No Solution:

Enter as a 3X4 matrix

Last row:

0 0 0 1

No Solution.

### Infinite Solutions:

Enter as a 3X4 matrix

Last row:

0 0 0 0

Infinitely Solutions

### Website to Visualize the Solutions

• http://www.cpm.org/flash/technology/3dsystems.swf

• Worksheet