A First Course in Linear Algebra · Problem LI.M21

Vectors — Robert Beezer

Mathematics — Linear Algebra · linear-independence-proofs

Problem

Suppose that

S = \{\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3\}

is a linearly independent set of three vectors from

\mathbb{C}^{873}

. Prove that the set

T = \{2\mathbf{v}_1 + 3\mathbf{v}_2 + \mathbf{v}_3,\ \mathbf{v}_1 - \mathbf{v}_2 + 2\mathbf{v}_3,\ 2\mathbf{v}_1 + \mathbf{v}_2 - \mathbf{v}_3\}

is linearly independent.