Warm-Up

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# Warm-Up - PowerPoint PPT Presentation

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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Presentation Transcript
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
How to set it up:

Old Way:

Coefficient

Variable

Constant

How to set it up:

***Notice there is

no more variable

the constant as an

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