# Linear transformations

Please help me solve the following linear algebra questions involving linear transformation and matrices. (see attached)

? Let and let . Define a map by sending a vector to .

a) let and be the standard basis vectors of V. let , and be the standard basis vectors of W. Find the matrix of T with respect to these bases of V and of W.

b) let and . Prove that form a basis of V and find the matrix of T with respect to the bases of V and of W.

c) let . Show that form a basis of W. Find the matrix of T with respect to the bases of V and of W.

? Let and let be the linear transformation given by

find the matrix A of T with respect to the standard basis

of both V and W.

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#### Solution Summary

There are a variety of linear transformation problems here, such as "find the matrix A of T with respect to the standard basis" as well as proofs that a given vectors is a basis