Ex. 1: Consider a 
matrix:
- Construct this matrix in Python using the function array.
- Construct the same matrix using the function arange followed by a suitable reshape.
- What is the result of the expression M[2,:]? What is the result of the similar expression M[2:]?
Ex. 2: Given a vector x, construct in Python the following matrix:
Here, 
are the components of the vector 
(numbered from zero). Given a vector 
, solve in Python the linear equation system 
. Let the components of 
be denoted by 
. Write a function poly, which has 
and 
as input and computes the polynomial:
Plot this polynomial and depict in the same plot the points 
as small stars. Try your code with the vectors:
Ex. 3: The matrix 
in Ex. 2 is called a Vandermonde matrix. It can be set up in Python directly with the command vander. Evaluating a polynomial defined by a coefficient vector can be done with the...