for course in Linear Algebra

1. Robert Geofroy

2. https://cloud.sagemath.com/

3. 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.

4. SAGE MathCoud
 Once in SAGEMathCloud, you will then be asked to
create a new project. Let’s create one for our Systems
of Linear equations

5. New SAGE worksheet..

6. SAGEMathCloud interface…

7. Systems of Linear Equations
 We 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.

8. Matrix Representation
 So 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:

9. How this looks in SAGEMath…

10. Solution
 As you can see,
SAGEMathCloud provides
us with the solution in line
12 of the output
x = -1 and y = -5
 This corresponds with what
we had worked out
manually.
 If we want, we can also
check the solution
graphically…

11. Thanks for watching!