Prove Theorem 1 4 Assume that V and W are vector spaces of dimensions n and m with bases B and D, and that h V W is a linear map If h is represented by and V is represented by then the representation of the image of is this h1,2 hi n ,TL h2 1 h22 hz m 1 RepB,D(11) hm,1 hm,2m,B,D C1 C RepB (V) Cn ,2C2 Repo( h(v) ) m,2C2

Question: Prove Theorem 1.4. Assume that V and W are vector spaces of dimensions n and m with bases B and D, and that h: V

Prove Theorem 1.4.
Assume that V and W are vector spaces of dimensions n and m with bases B and D, and that h: V †’ W is a linear map. If h is represented by

and ˆˆ V is represented by

then the representation of the image of is this.

h1,2 hi.n ,TL h2.1 h22 .. hz.m 1 .. RepB,D(11) = hm,1 hm,2m,B,D C1 C? RepB (V)- Cn ,2C2 Repo( h(v) ) = m,2C2

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