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    Linear transformations

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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 February 24, 2021, 2:31 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/linear-transformations-26591

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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

    $2.19

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