using sage maths to solve systems of linear equations
TRANSCRIPT
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Using SAGE Maths (Cloud) to solve Systems of Linear
EquationsRobert Geofroy
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https://cloud.sagemath.com/
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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.
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SAGE MathCoudOnce in SAGEMathCloud, you will then be
asked to create a new project. Let’s create one for our Systems of Linear equations
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New SAGE worksheet..
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SAGEMathCloud interface…
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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.
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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:
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How this looks in SAGEMath…
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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…
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Thanks for watching!