(参考)Python：FEMでの疎行列計算の利用（３次元骨組構造解析での事例）＞簡単な連立一次方程式を解いてみる（１）
https://qiita.com/damyarou/items/85c7902cc658d748115e
(参考)Sparse Matrices
http://docs.sympy.org/latest/modules/matrices/sparse.html

fullscript.py

from sympy import *
var("A B C")
A=Matrix(([ 1,  5,  0,  0,  0],
          [ 0,  2,  8,  0,  0],
          [ 0,  0,  3,  9,  0],
          [ 0,  0,  0,  4, 10],
          [ 0,  0,  0,  0,  5]))

B =Matrix(([1],[2],[3],[4],[5]))
C=A.inv() * B
print("C=[",float(C[0]),float(C[1]),float(C[2]),float(C[3]),float(C[4]),"]")
# C=[ 106.0 -21.0 5.5 -1.5 1.0 ]