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Pre calculus warm up3.11.14
C. How many solutions are there to each 3 - variable system graphed below?
A. The graph of a 3 variable equation is a _____________?
B. What is row-echelon form?
Gaussian Elimination
GENERAL IDEA:1. Forward Elimination2. Back Substitution
GOAL: Transform the system into Row-echelon form.
HOW: Perform elementary row operations so that back substitution can be easily done.
Elementary Row Operations
Changes done to a system of equations that still maintain its equivalence.There are only 3 Elementary Row Operations1. Interchange 2 equations (or Rows)2. Multiply one of the equations (or rows) by a
non-zero constant.3. Add a multiple of one row to another.
Gaussian Elimination
Perform elementary row operations so that back substitution can be easily done.
Suggested steps:1. Obtain a coefficient of “1” for x in Row 12. Eliminate x from Row 2 and Row 33. Obtain a coefficient of “1” for y.4. Eliminate y from Row 35. Obtain a coefficient of “1” for z – then back substitute
to solve.