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.