Linear Algebra Help - Pythagorem Theorem

[eunhye732]

I have been trying to figure this out but can't. I even went to the tutorial but the lady kept mumbling so it was obvious that she didn't really know how to do it either. So I really hope someone could help me. The only thing he told me was to look at the pythagorem theorem. Thanks

 

[mathwonk]

what is the question? i cannot read the scan.

 

[HallsofIvy]

The question is to show that norm(v over norm(v))= 1 for v a vector.
That is, that
$$\left|\left|\frac{v}{\left|\left|v\right|\right|}\right|\right|= 1$$
eunhye732, one of the things you certainly should have learned about the "norm" is that ||av||= |a| ||v|| for a any number and v a vector. In particular, if a is a positive number then ||av||= a ||v||.
Think about that with a= 1/||v||.

 

[eunhye732]

The question is to show that norm(v over norm(v))= 1 for v a vector.
That is, that
$$\left|\left|\frac{v}{\left|\left|v\left|\left|}\left|\left|= 1$$
eunhye732, one of the things you certainly should have learned about the "norm" is that ||av||= |a| ||v|| for a any number and v a vector. In particular, if a is a positive number then ||av||= a ||v||.
Think about that with a= 1/||v||.

Oh i see how to do it now.
That helped a lot.
Thanks so much!