Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources

Course: Algebra I / Elementary Algebra
Topic: Linear Systems
Subtopic: 3x3 Systems - Electronically

Overview

Solving 3x3 (or larger) linear systems algebraically is very time-consuming so why not take advantage of technology to solve them?

Solving a linear systems electronically (on a handheld grapher or using a system solver program) requires using a command called RREF. How you do this will depend what technology you have available to you. See the supplemental resources below for suggestions.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 5.6.1 Determine if a given ordered triple (x,y,z) is a solution to a given 3x3 system or not by algebraically "checking" it in the system's equations
• 5.6.2 Solve 3x3 and larger linear systems electronically using a system solver (RREF)
• 5.6.3 When solving a system electronically using RREF, recognize consistent, inconsistent, and dependent systems

Terminology

Define: dimension (order; size) of a system, 3x3 system (and 4x4 system, etc.), augmented matrix, row reduced echelon form (RREF)

Text Notes

For 3x3 and larger systems you must be able to recognize the inconsistent and dependent types electronically based on the last line of the result from RREF (more on this in class).

Geometrically it is neat to look at the 3x3 systems of intersecting planes but if you don't completely understand them, no worries, this is covered in later courses.

SKIP any "modeling" applications. This includes problems of the form, "Find the quadratic function y=ax2+bx+c whose graph passes through the given points."

Supplementary Resources

You must be able to use a calculator (handheld or software) to solve a larger linear system electronically (using the RREF system solver command).

If you don't have a handheld graphing calculator then RREF can be performed using the Online Row Reducer. ⇐ Useful!

If you have a handheld graphing calculator then these sites may help: