MATH 310
Homework due 06/15/2011
1. Show that the set of complex numbers Cis a vector space by using
the addition of complex numbers as the addition of vectors and the
product of a real number by a complex number as the scaling of a
vector by a number.
2. Show that if λv= 0 in a vector space Vif and only if λ= 0 or v=0.
3. Let Vbe a vector space and u,vbe two vectors in V. Then, show
that there exists a vector win Vwith
u+w=v
4. Let Vbe a vector space and uis in V. If λis a real number, then:
(−λ)(−u) = λu
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