##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 |