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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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Presentation Transcript
warm up
Warm-Up
  • Solve the following system of equations:
learning targets
Learning Targets
  • Possible solutions for a system
  • The differences between RREF and Inverse Multiplication
  • Using Reduced Row Echelon Form to solve systems
quick recap
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
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
How many types of solutions can we have?
  • Pause and Ponder, SILENTLY!
  • One Solution
  • No Solution
  • Infinite Solutions
example
Example

Solve using Inverse Multiplication:

What Does it Mean?!?

example1
Example

Solve using Inverse Multiplication:

AGAIN!?!

problems with inverse multiplication
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?
slide10
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
How to set it up:

Old Way:

Coefficient

Variable

Constant

how to set it up1
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
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
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
No Solution:

Enter as a 3X4 matrix

Last row:

0 0 0 1

No Solution.

infinite solutions
Infinite Solutions:

Enter as a 3X4 matrix

Last row:

0 0 0 0

Infinitely Solutions

website to visualize the solutions
Website to Visualize the Solutions
  • http://www.cpm.org/flash/technology/3dsystems.swf
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