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

prsategazd 2022-01-05 Answered
Let V, W, and Z be vector spaces, and let T:VW and U:WZ be linear.
If UT is onto, prove that U is onto.Must T also be onto?
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Marcus Herman
Answered 2022-01-06 Author has 41 answers
Let UT is onto.
It is needed to prove that U is onto.
Let zZ then for some xV.
UT(x)=z but T(x)W.
So U is onto.
But T may not be onto.
Let T:RR2 be T(x)=(x,y) and U:R2R be U(x.y)=0.
Therefore, T may not be onto.
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