Suppose for and is a linear transformation.
Domain
Codomain
for
and
.
The set of vectors is (select all that apply):
A.
linearly independent
B.
a basis for the codomain
C.
a spanning set
D.
a basis for the domain
E.
none of these
The set of vectors is (select all that apply):
A.
linearly independent
B.
a spanning set
C.
a basis for the domain
D.
a basis for the codomain
E.
none of these
The linear transformation is (select all that apply):
A.
surjective (onto)
B.
bijective (an isomorphism)
C.
injective (one-to-one)
D.
none of these
Using that is a linear transformation, find . Enter your answer as a coordinate vector such as <1,2>.
Find the matrix for the linear transformation (relative to the standard basis in the domain and codomain). That is, find the matrix such that . For instance, enter [ [1,2], [3,4] ] for the matrix .
You can earn partial credit on this problem.