Question

a) A vector is a directed line segment (an arrow).<False>

b) A vector is an n-tuple of real numbers. <False>

c) A vector is any element of a vector space <True>

d) There is a vector space consisting of exactly two distinctvectors. <False>

e) The set of polynomials with degree exactly 1 is a vectorspace under the operations defined by (a0+a1x) + (b0+b1x) = (a0+b0)+ (a1+b1x) and k((a0+a1x) = (ka0) +(ka1)x. <False>

The answers above are from the textbook itself. Why (a), (b), (d)and (e) are false??? I need explanation in details, and a counterexample of them will be very helpful. Thanks!