Answer
a. True
b. True
c. False
d. True
e. True
Work Step by Step
a. True, this is the definition of a vector
b. True, by the algebraic properties of vectors: $(u-v)+v = (u + (-v)) + v = u + (-v + v) =u$
c. False, the zero vector is always in the span of a set of vectors.
d. True, the line through $u$ and the origin, is the vectors formed by a linear combination of $u$ and $v$ where the coefficient on $u$ is any real number and the coefficient on $v$ is $0$.
e. True, this follows from the definition of span
