12 September 2014
1) Let V be the vector space of all functions from R into R; let Ve be the subset of even functions ,
f(–x)=f(x); let Vo be the subset of odd functions, f(–x)=–f(x)
- Prove that Ve and Vo are subspaces of V.
- Prove that Ve+Vo=V.
- Prove that Ve ∩ V0= {0}.
2) In V3(R),where R is the field of real numbers, examine the following sets of vectors for linear independence:
- {(1,3,2),(1,-7,-8),(2,1,-1)};
- {(1,2,0),(0,3,1),(-1,0,1)}.
3) Find a linearly independent subset T of the set S={α1,α2,α3,α4} where α1=(1,2,-1),α2=(-3,-6,3), α3=(2,1,3),α4=(8,7,7)єR3 which spans the same space as S.
