Question

Let T: U--> V be a linear transformation. Prove that the range of T is a subspace of W

Answer #1

in your given question there is a mistake.you given T:U to V then range T is a subspace of V not W.so i take T:V to W and i prove range T is a subspace of W.(if you have T:U to V then replace V by U and W by V in my proof)

Proof:

Here we prove three results

1) for any two vectors in range T we prove their sum is also in range T

2) T(0) is in range T

3) let c be a scalar and w is a vector in V then we prove cw is in range T

So range T is a subspace of W.

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