 
Summary: Linear Algebra Worksheet 4
Math 108A Fall 2009, TA Grace Kennedy
NAME:
Course Website: http://math.ucsb.edu/kgracekennedy/F09108A.html
Supplemental Reading: Axler Chapter 23
Linear Transformations
V and W are both finite dimensional vector spaces.
1. Give an example of a linear map from R4
to R3
and an example of a
nonlinear map.
(a) Can you have a linear map that is surjective? If so, give one and
show it is surjective; if not, show why.
(b) Can you have a linear map that is injective? If so, give one and show
it is injective; if not show show why.
(c) Can you have a linear map that is bijective? Why or why not?
2. Give an example of a linear map from R3
to R4
and an example of a
nonlinear map.
