# coding: utf-8

# # Elimination Matrices I: The Basics

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import numpy as np


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n = 4


# ----------------
# Let's create an elimination matrix as $M$:

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M = np.eye(n)
M[1,0] = 2
M


# Here's a matrix $A$. See if $M$ has the desired effect on $A$:

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np.random.seed(5)
A = np.random.randn(n, n).round(1)
A


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M.dot(A)


# -----------------------
# Next, see if you can build the inverse of $M$:

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Minv = np.eye(n)
Minv[1,0] = -2
Minv


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M.dot(Minv)