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


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.


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


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: