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Show that L: V -> W is a linear transformation if and only if

L(au + bv) = aL(u) + bL(v) for any scalars a and b and and any

vectors u and v in V.

For L(au +bv), this is my proof. (Is this wrong?)

L(au + bv) = L [ a(a', b', c') + b(a'', b'', c'')]

= L [ aa' + ba'', ab' + bb'', ac' + bc'' ]

= (aa' + ab' + ac') + ( ba" + bb" +bc")

= a(a' + b' +c') =b(a" + b" + c")

= aL(u) + bL(v)

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# Homework Help: Proving linear transformation

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