16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 2.2.6

Vector Spaces

Mathematics — Linear Algebra · subspaces-of-low-dimensional-spaces

Problem

(a) Prove that the only subspaces of

R^1

are

R^1

and the zero subspace. (b) Prove that a subspace of

R^2

R^2

, or the zero subspace, or consists of all scalar multiples of some fixed vector in

R^2

. (The last type of subspace is, intuitively, a straight line through the origin.) (c) Can you describe the subspaces of

R^3