Linear systems have zero, one, or infinitely many solutions.

math.la.t.linsys.zoi


Sage cell illustrating creating a coefficient matrix of a system of three equations in three variables, augmenting with a vector of constants, and bringing the matrix to reduced row-echelon form in order to find the (unique) solution.

License
GFDL-1.3
Created On
December 30th, 2016
3 years ago
Views
3
Type
 SageMath Cell
Timeframe
 Post-class
Perspective
 Example
Language
 English
Content Type
application/octet-stream

A 3x3 system having a unique solution is solved by putting the augmented matrix in reduced row echelon form. A picture of three intersecting planes provides geometric intuition.

Created On
February 15th, 2017
3 years ago
Views
2
Type
 Video
Timeframe
 Review
Perspective
 Example
Language
 English
Content Type
text/html; charset=utf-8

Sample problems to help understand when a linear system has 0, 1, or infinitely many solutions.

Created On
February 15th, 2017
3 years ago
Views
2
Type
 Handout
Timeframe
 In-class
Perspective
 Example
Language
 English
Content Type
text/html; charset=utf-8

We will now be more careful about analyzing the reduced row-echelon form derived from the augmented matrix of a system of linear equations. In particular, we will see how to systematically handle the situation when we have infinitely many solutions to a system, and we will prove that every system of linear equations has either zero, one or infinitely many solutions. With these tools, we will be able to routinely solve any linear system.

License
GFDL-1.2
Submitted At
September 11th, 2017
 3 years ago
Views
3
Type
 Textbook
Language
 English
Content Type
text/html