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numpy Homework


Implement the following python functions. The name of the exercise should be the name of the function. You will need import numpy! On your own computer I recommend Anaconda because it is installed with numpy by default. Mind that you need the 2.7 version. Or you can use the leibniz.

matrix (2p)

The function should have 3 parameters, one matrix and two indices:

  M: a matrix
  i: a row index
  j: a column index

The output should be a matrix (let's call A) with the same size as M. It should be the outer product of the ath row and the ath column of M. In formula:

A_{i,j} = M_{i, b}\cdot M_{a, j}

You can calculate this kind of product of vectors by multiplying a somethig-by-1 and a 1-by-something matrix.

derivative (3p)

The function should have 3 parameters, two real numbers and one integer:

  a: the left-hand-side of the interval
  b: the right-hand-side of the interval
  n: the number of uniformly distributed points in the interval

a < b and n > 1.

  • The output should be a numpy vector of length n-2 containing the numerical derivative of the function x\cdot e^x on the given interval, except the endpoints.
  • Use the following estimation for the derivative (more about numerical differentiation):

{\Delta f}_i = \frac{f(x_{i+1})-f(x_{i-1})}{x_{i+1}-x_{i-1}}


Send the exercises as a python code from your math email account to

You should attach one python file containing the definition of the required functions without any test code or print command.

The file should be named:

  EN1_HW8_<user account>.py

the subject of the letter should be the same (without the extension). For me example:


12th of May, 29:59

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