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: No Solution.
Infinite Solutions: Enter as a 3X4 matrix Last row: 0 0 Infinitely Solutions
You Try using RREF:
Website to Visualize the Solutions
For the weekend… Worksheet