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Let T : R3 → R2 be a linear map. Recall that the image of T, Im(T), is the set {T(i) : R*) (a) Suppose that T(v)- Av. Describe the image of T in terms of A Using this description, explain why Im(T) is a subspace of R2. (b) What are the possible dimensions of Im(T)? (c) Pick one of the possible dimensions and construct a specific map T so that Im(T) has that dimension.

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(a) niven, TV)- Av .|In(t) is a subspace of R2- , hence Im(T) i* a non emp , 5 there ests Vand V2 in and AV2 -U R Such that AV 2. Henie, Im(T) i a subspaie of R2 we see that Im (T) İga su b s paie of R2 ension of IR2 2. Now, climen Sio of an Subspace of Can beO, dr° 2,5o dimensjon of Im(T) Can be o, on 2 0 0 o Let, A =1000 Hene, In(t) = 59, dimension of 1m(T)=0

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