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    linear transformation

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    For each of the following functions decide whether or not the function is a linear transformation. Prove your answer in each case:
    (a) F: V3(R) --> V2(R) defined by F(a1, a2, a3) = (2a1 - a2, 3a3)
    (b) G: V3(R) --> V2(R) defined by G(a1, a2, a3) = (a1 - a2 + a3, a1 + a2a3)

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    Please find the solutions/explanations attached herewith.

    I hope it will help.


    Solution part(a):
    Let u = (u1, u2, u3) and v = (v1, v2, v3)
    (u + v) = (u1+v1, u2+v2, u3+v3)
    F(u + v)
    = F(u1+v1, u2+v2, u3+v3)
    = (2(u1+v1)-(u2+v2), 3(u3+v3))
    F(u) = (2u1 -u2, ...

    Solution Summary

    A linear transformation is embodied.