Let V, W, and Z be vector spaces, and let



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Let V, W, and Z be vector spaces, and let T:VW and U:WZ be linear.
If U and T are one-to-one and onto, prove that UT is also

Answer & Explanation



Beginner2022-01-08Added 34 answers

Let U and T is one to one.
Assume, UT(x)=UT(y)
T(x)=T(y) U is one to one
x=y T is one to one
So, if U and T is one to one, then UT is also one to one.
Suppose U and T is onto, then by definition of onto T(x)=y, for all y W and
U(y)=z for all zZ.
So, that UT is onto.
Hence, UT is onto.

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