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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.© BrainMass Inc. brainmass.com March 6, 2023, 12:50 pm ad1c9bdddf
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