A First Course in Linear Algebra · Problem SS.T21

Vectors — Robert Beezer

Mathematics — Linear Algebra · spanning-sets-proofs

Problem

Suppose that

S

is a set of vectors from

\mathbb{C}^m

and

\mathbf{x}, \mathbf{y} \in \langle S \rangle

. Prove that

\mathbf{x} + \mathbf{y} \in \langle S \rangle