Step 1
the set of linear transformations together with the usual addition and scalar multiplication of functions are clearly defined.
next we need to determine if the five conditions of Definion 7.1 are all met.
If and are a linear transformation if for all vectors u and v and then their sum will also be a linear transformation in , that is, is closed under addition.
If is a linear transformation if for all vectors u in and c is a scalar then i and will also be a linear transformation thus is also closed under scalar multiplication.
M If is an identical zero transformation, then if is in linear transformation, then for all in , so that is the zero transformation.
If linear transformation, it has its inverse linear transformation so that
Step 2
a) We are checking whether you are
Therefore, commutativity is valid.
b) Check
Not exactly what you’re looking for?
Ask My Question