Ex. 1 → Consider a 4 × 3 matrix M:
- 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 expressionM[2:]
?
Ex. 2 → Given a vector x, construct in Python the following matrix:
Here, xi
are the components of the vector x (numbered from zero). Given a vector y, solve in Python the linear equation system Va = y. Let the components of a be denoted by ai, i = 0, ..., 5. Write a function poly
, which has a and z as input and which computes the polynomial:
Plot this polynomial and depict in the same plot the points (xi , yi ) as small stars. Try your code with the vectors:
- x = (0.0, 0.5, 1.o, 1.5, 2.0, 2.5)
- y = (-2.0, 0.5, -2.0, 1.0, -0.5, 1.0)
Ex. 3 → The matrix V in Ex. 2 is called a Vandermonde matrix. It can be set up in Python directly by the command vander
. Evaluating a polynomial defined by a coefficient...