Using Rule of Sarrus, Cramer's Rule, and Python to Solve a System of Three Linear Equations
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Permalink
Failed to load latest commit information.
.gitignore
LICENSE
README.md
sclinear.py

README.md

sarrus_cramer

##Using Rule of Sarrus, Cramer's Rule, and Python to Solve a System of Three Linear Equations

# System of three linear equations
# ax + by + cz = j
# dx + ey + fz = k
# gx + hy + iz = l

# System of three linear equations in matrix notation
#  -         -   - -       - -
# | a   b   c | | x |     | j |
# |           | |   |     |   |
# | d   e   f | | y |  =  | k |
# |           | |   |     |   |
# | g   h   i | | z |     | l |
#  -         -   - -       - -

# Matrix of Coefficients
# a b c
# d e f
# g h i

# Matrix of Variables
# x
# y
# z

# Matrix of Resulting Values
# j
# k
# l

# Rule of Sarrus
# a b c|a b
# d e f|d e
# g h i|g h

# Rule of Sarrus Index Values
# 0 1 2|0 1
# 3 4 5|3 4
# 6 7 8|6 7

# Determinant
# det(M) = aei + bfg + cdh - gec - hfa - idb

# Cramer's Rule
# | j b c |   | a j c |   | a b j |
# | k e f |   | d k f |   | d e k |
# | l h i |   | g l i |   | g h l |
# ---------,  ---------,  ---------
# | a b c |   | a b c |   | a b c |
# | d e f |   | d e f |   | d e f | 
# | g h i |   | g h i |   | g h i |