The standar bassis vectors for are given by

For a vector

We have that 1.

We define the vectors in :

a) Use Python to show that the vectors are perpendicular to each other

b) Find an (3 3)-matrix A so that for j = 1, 2, 3. and show that for an vector

We get

c) Use Python to find the inverse matrix B for A. Vertify in Python that for j = 1, 2, 3.

d) Let . Define a vector by

Explain why we have