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Unformatted text preview: map R : U V such that RS = T . Prove all of your claims. (4) Let X be a nitedimensional vector space over K and let { x 1 ,...,x n } be an ordered basis for X . Let U be a vector space over the same eld K but possibly with a dierent dimension, and let { u 1 ,...,u n } be an arbitrary set of vectors in U . Show that there is precisely one linear transformation T : X U such that Tx i = u i for each i = 1 ,...,n ....
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 Spring '08
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 Linear Algebra, Algebra

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