# Warm-Up. Reduced Row Echelon Form (RREF) Learning Targets  Possible solutions for a system  The differences between RREF and Inverse Multiplication.

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Warm-Up

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

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: CoefficientVariable Constant

How to set it up: Coefficient Constant ***Notice there is no more variable matrix and we add the constant as an additional column.

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 Infinitely Solutions

You Try using RREF:

Website to Visualize the Solutions  http://www.cpm.org/flash/technology/3dsystems.swf http://www.cpm.org/flash/technology/3dsystems.swf

For the weekend…  Worksheet

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