The standar bassis vectors for are given by

For a vector We have

We define the vectors in :

1)Use Python to show that the vectors vj are mytally perpendicular to each other, and find an (3 3)-matrix A so that for j = 1, 2, 3. show that for an vector

so that we have

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

And Let . Define a vector by

And explain why we have