Using SAGE Maths (Cloud) to solve Systems of Linear

EquationsRobert Geofroy

https://cloud.sagemath.com/

What is SAGEMathCloud?Sage is a software for collaborative computational mathematics

It is free, open-source math software that supports research and teaching in algebra, geometry, number theory, cryptography, numerical computation, and related areas.

It is a cloud based application.

SAGE MathCoudOnce in SAGEMathCloud, you will then be

asked to create a new project. Let’s create one for our Systems of Linear equations

New SAGE worksheet..

SAGEMathCloud interface…

Systems of Linear EquationsWe may be familiar with these systems from

our secondary school in what we know as simultaneous equations.

For instance, we may have the following problem:

3 x - y = 2 … (1) x + y = -6 …(2)

This is a very simple system and we can easily solve this by the normal elimination method and we will see that the solution is x = -1 and y = -5.

Matrix RepresentationSo we have the system (only two equations

in two variables but the same principles apply for three, four and more:

3 x - y = 2 … (1) x + y = -6 …(2)

The system can be represented by the following matrix equation:

How this looks in SAGEMath…

SolutionAs you can see,

SAGEMathCloud provides us with the solution in line 12 of the output

x = -1 and y = -5This corresponds with

what we had worked out manually.

If we want, we can also check the solution graphically…

Thanks for watching!