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For questions on linear algebra, including vector spaces, linear transformations, systems of linear equations, spanning sets, bases, dimensions and vector subspaces.

3 votes
2 answers
326 views

How to show that $Im(f) = B$ iff $f$ is onto?

Let $f : A → B$ My teacher said that $\text{Im}(f)=\{f(b):b\in A\} = B$ iff $f$ is onto. I know that this statement is true because it is kind of obvious but is there a way to prove it?
gbd's user avatar
  • 2,013
0 votes
0 answers
253 views

Dual Space of $R^{n}$? [duplicate]

My teacher said (without explaining why) that because $R^{n}$ is finite dimensional then set of all linear functions (Dual space) is equal to the set of all continuous linear functions. Can someone ex …
gbd's user avatar
  • 2,013