Please see the attached file for full problem description.
The "norm" of a vector is a measure of it's "size" or "magnitude". There are many different ways to express the norm of a vector. These are referred to as the Lk norm, and written....see attached
Because, L1 is the linear combination fo mods of v1 to vn hence this is linear transformation of all the vi (i = 1 to n).
In case of L2 norm of v is root of sum of ...
This defines norms and asks whether they are linear transformations and one-to-one mappings