Currently taking my math exam, can soneone help me do a few of

>>257553
So wird das nichts mit deinem Abi

>>257572
Hallo, meine Deutsch ist nicht Gut. Was ist das "Abi" en Englisch?

>>257574
I assumed you were a German student doing the final exam at the end of school year 12, called the Abitur, which is equivalent to A-levels in other countries.
Why are your questions in German if you are not German?

>>257595
klingt nach heutigem deutsch für mich,traurigerweise

>>257595
I think it's first year linear algebra (Matrikel, Übungsnummer).

1) Linear means that f(kx) = kf(x) and f(x1 + x2) = f(x1) + f(x2). Easy to check.

2) You only need to check if Ui is closed under the scalar multiplication and addition, and is not empty. Also each Ui must contain the zero vector (0,0,0) which immediately shows that two of the Ui cannot be subspaces of R^3.

3) rg f is the dimension of the image of f. f is a permutation of the components of v, I'm not sure about g.

4) Which basic vector space has no three linear independent vectors? Can you find three vectors a,b,c such that every pair of vectors is linear independent?