PRE-AP PRE-CALCULUS CHAPTER 7, SECTION 3 Multivariate Linear Systems and Row Operations 2013 - 2014.

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Presentation transcript:

PRE-AP PRE-CALCULUS CHAPTER 7, SECTION 3 Multivariate Linear Systems and Row Operations

TRIANGULAR FORM FOR LINEAR SYSTEMS

SOLVING BY SUBSTITUTION

GAUSSIAN ELIMINATION You can transform a system of equations to the triangular form by using Gaussian Elimination. Gaussian Elimination is named after the famous German mathematician Carl Friedrich Gauss (1777 – 1855). Gauss is known for proving that every algebraic equation has at least one root or solution (the fundamental theorem of Algebra), as well as work in physics and astronomy. Gauss is considered by many to be one of the three greatest mathematicians along with Newton and Archimedes.

HOW TO USE GAUSSIAN ELIMINATION

USING GAUSSIAN ELIMINATION

FINDING NO SOLUTION

SOLVING A SYSTEM USING THE CALCULATOR Solving systems using a matrix in your calculator:

SOLVE THE SYSTEM USING YOUR CALCULATOR

FINDING INFINITELY MANY SOLUTION

FITTING A PARABOLA TO THREE POINTS

CH. 7.3 HOMEWORK Pg. 604 – 605 #’s: 1, 4, 5, 7 – use method listed in instructions #’s: 35, 38, 39, 40, 42, 43 – ignore the book directions, just solve each system using the matrix function in your calculator #67 – show your work (matrix) that you will use