Linear Algebra (Vector)

Question

Determine whether or not the set of vectors identified is a subspace of:

#1.

R³ if U={vectors whose length does not exceed 1} , i.e., U= {(a, b, c): a² + b² + c² ≤1}

Answer 1

U is not a subspace of R³ because U is not closed under scalar multiplication.

For example, v = <1/2, 0,0 > is in U but 3v = <3/2, 0, 0> is not.