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Warm-Up

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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  1. Warm-Up • Solve the following system of equations:

  2. Reduced Row Echelon Form (RREF)

  3. Learning Targets • Possible solutions for a system • The differences between RREF and Inverse Multiplication • Using Reduced Row Echelon Form to solve systems

  4. 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

  5. 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

  6. How many types of solutions can we have? • Pause and Ponder, SILENTLY! • One Solution • No Solution • Infinite Solutions

  7. Example Solve using Inverse Multiplication: What Does it Mean?!?

  8. Example Solve using Inverse Multiplication: AGAIN!?!

  9. 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?

  10. 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

  11. How to set it up: Old Way: Coefficient Variable Constant

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

  13. 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.

  14. 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

  15. No Solution: Enter as a 3X4 matrix Last row: 0 0 0 1 No Solution.

  16. Infinite Solutions: Enter as a 3X4 matrix Last row: 0 0 0 0 Infinitely Solutions

  17. You Try using RREF:

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

  19. For the weekend… • Worksheet

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