If sequence of vector spaces is exact then the sequence of duals is also exact

196 Views Asked by At

Induced Exact Sequence of Dual Spaces

I was able to prove the result for short exact sequences, but my instructor did not say short exact sequence, just sequence. So it is not given that the maps in the sequence are injective or surjective. Is there a counterexample to the sequence of duals being exact if g in

$V \xrightarrow{f} V' \xrightarrow{g} V''$ is not surjective?