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## PowerPoint Slideshow about ' Warm-Up' - phelan-vaughn

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Presentation Transcript

Warm-Up

- Solve the following system of equations:

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

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:

***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

Website to Visualize the Solutions

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

For the weekend…

- Worksheet

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