Question

in linear algebra any vector space example ,how we solve it without solving all its axioms ?.
Let V be a set on which addition and scalar multiplication are defined (this means that if u and v are objects in V and c is a scalar then we’ve defined and cu in some way). If the following axioms are true for all objects u, v, and w in V and all scalars c and k then V is called a vector space and the objects in V are called vectors.

(a)u+v is in V This is called closed under addition.
(b) cu is in V This is called closed under scalar multiplication.
(c) u+v=v+u
(d) u+(v+w)=(u+v)+w
(e) There is a special object in V, denoted 0 and called the zero vector, such that for all u in V we have u+0=0+u=u.
(f) For every u in V there is another object in V, denoted and called the negative of u, such that .u-u=u+(-u)=0
(g) c(u+v)=cu+cv
(h) (c+k)u=cu+ku
(i) c(ku)=(ck)u
(j) 1u=u
plz tell me how we can solve problem with shortcut , not using all these axioms.

problem:Let Pn(F) consist of all polynomials in P(F) having degree less than
or equal to n. Show that Pn(F) is a subspace of P(F).

Answer 1

explain a question a bit more... what kind of problems..what axioms...talking about quantum mechanics ?

Answer 2

ok.......now plz tell the ans

Answer 3

I need to work out..go through some book.. can't readily solve this problem here as it is bit abstract...sorry

Answer 4

ok .... no problem