$1$ Introduction to python with Linear Algebra

We start with some simple numeric task in python using numpy. Remember to include the numpy

package in your python script like this:

import numpy as np

A beginner guide to numpy is found here Numpy quick start

Define variable $x=\frac{}{2}.$ Compute the result of $y=x+sin(x)+2cos(x)+\frac{1}{2}*x^2$ and store it in

a variable denoted $y$

Compute a new variable $z$ defined by $z=y^3+2\mathrm{.}5*cos(y)$

Define the vector with dimensions $R^{mxn}=R^{6x1}$ where $m$ represents rows $($horizontal$)$ and $n$

represents columns $($vertical$).$

$x=\left[\begin{array}{c}1\\ 0\\ 0\\ 1\\ 0\\ 0\end{array}\right]in{R}^{61}$

Define the row vector

$b=\left[\begin{array}{cccccc}0& 1& 1& 1& 1& 1\end{array}\right]in{R}^{16}$

Next, define the matrices $Ain{R}^{610},Bin{R}^{62},Cin{R}^{66}$ in python

$A=\left[\begin{array}{cccccccccc}1& 0& 1& 1& 1& 0& 0& 0& 1& 1\\ 1& 1& 1& 0& 1& 0& 1& 0& 1& 0\\ 0& 0& 1& 1& 1& 0& 1& 1& 1& 1\\ 1& 0& 0& 1& 1& 1& 1& 0& 1& 0\\ 1& 1& 1& 1& 1& 1& 1& 0& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right],B=\left[\begin{array}{cc}1& 0\\ 1& 1\\ 0& 0\\ 0& 1\\ 1& 0\\ 1& 1\end{array}\right],C=\left[\begin{array}{cccccc}0& 1& 1& 1& 1& 1\\ 1& 0& 0& 0& 1& 1\\ 1& 0& 1& 0& 1& 1\\ 0& 1& 1& 1& 0& 1\\ 1& 0& 0& 1& 0& 1\\ 1& 1& 1& 1& 1& 1\end{array}\right]$