Solving Linear Equations with Python
[Pages:20]
Solving Linear Equations with Python
Hans-Petter Halvorsen
Free Textbook with lots of Practical Examples
Additional Python Resources
Contents
? Linear Equations ? NumPy ? NumPy.linalg ? Least Square Method
Linear Equations in Python
? Python can be used to solve a large amount of linear equations using built-in functions
? Typically, you will use the NumPy library
NumPy
? The Python Standard Library consists basic Math
functions, for more advanced Math functions, you
typically want to use the NumPy Library
? If you don't have Python yet and want the
simplest way to get started, you can use the
Anaconda Distribution - it includes Python,
NumPy, and other commonly used packages for
scientific computing and data science.
? Or use "pip install numpy"
Linear Equations
Given the following linear equations:
!!! + !"" + !## + = ! "!! + "!" + "## + = "
These equations can be set on the following general form:
=
Where A is a matrix, x is a vector with the unknowns and b
is a vector of constants
"" "# =
$" $#
"
=
%
$
"
=
%
$
Solution: = !" (assuming !" is possible )
Example
Given the following linear equations: " + 2% = 5 3" + 4% = 6
Let's solve these equations manually
From eq(1) we get: " = 5 - 2% We put this in eq(2):
3(5 - 2%) + 4% = 6
This gives:
15 - 6% + 4% = 6 15 - 2% = 6 15 - 6 = 2%
2% = 9 9
% = 2 = 4.5
" = 5 - 9 = -4
Final solution: " = -4 % = 4.5
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