Inverse Matrix in Python

Question

My understanding is that I can use Python to initialize my matrix and then apply an inverse function to find the solution.

Answer 1

You can use matlab but:

1.) you will get a numerical approximation of the inverse,

2.) you won't learn anything from that.

Rather, try doing what the question asks you - work out what $z_1, z_2, z_3$ are in terms of $b_1, b_2, b_3$ (by writing out the equations and rewriting them a bit) or use any other technique to calculate an inverse of $3\times3$ matrix.

Answer 2

I'm not sure I understand your notation:

deltaz = [-1 1 0][z1] = [z2 - z1] = [b1] = b [0 -1 1] [z2] [z3 - z2] [b2] [0 0 -1] [z3] [0 - z3] [b3]

Are you attempting Python pseudocode or are you defining a matrix? If the latter, please use MathJax for a more readable format.

Answer 3

Expand the three linear equations and solve the system (by hand!). This is quasi-immediate.

Answer 4

Inverting a matrix:

import numpy as np

a = np.matrix([[-1, 1, 0],[0,-1,1],[0,0,-1]])
b = numpy.linalg.inv(a)

print(a)
print(b)

print(a*b)

the output should be:

[[-1  1  0]
 [ 0 -1  1]
 [ 0  0 -1]]

[[-1. -1. -1.]
 [-0. -1. -1.]
 [-0. -0. -1.]]

[[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

In case of a system of linear equations use an NumPy-Array for your vector:

import numpy as np

a = np.matrix([[-1, 1, 0],[0,-1,1],[0,0,-1]])
b = np.array([20,26,33])

solution = np.linalg.inv(a).dot(b)
```