Suppose is a matrix and
, , and .
What is ? Enter your answer as a coordinate vector of the form <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 .
Find a formula for the linear transformation . Enter your answer as a coordinate vector with the variables , , and in its components.
Find bases (i.e., maximal independent sets) for the kernel and image of . Please enter your answers as comma separated lists of vectors of the form <1,2> or <1,2,3>, as appropriate.
The linear transformation is (select all that apply):
A.
bijective (an isomorphism)
B.
surjective (onto)
C.
injective (one-to-one)
D.
none of these
You can earn partial credit on this problem.