ANSWER BOTH QUESTIONS ACCRUATELY AND CORRECTLY FOR A GOOD RATING Q5. Consider any vector space
V
. Let
x,y,z
be elements of
V
and
a,b
be scalars. (a) Prove: If
x+y=x+z
then
y=z
. (b) Prove:
(a+b)(x+y)=ax+bx+ay+by
. Q6. Consider polynomials with complex coefficients and degree at most
n
.
P_(n)(C)={a_(0)+a_(1)x+a_(2)x^(2)+cdots+a_(n)x^(n):a_(i)inC}
Prove that
P_(n)(C)
is a vector space. (Hint: summation notation will simplify your argument.)