A First Course in Linear Algebra · Problem LI.T15

Vectors — Robert Beezer

Mathematics — Linear Algebra · linear-independence-proofs

Problem

Suppose that

\{\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \ldots, \mathbf{v}_n\}

is a set of vectors. Prove that

\{\mathbf{v}_1 - \mathbf{v}_2,\ \mathbf{v}_2 - \mathbf{v}_3,\ \mathbf{v}_3 - \mathbf{v}_4,\ \ldots,\ \mathbf{v}_n - \mathbf{v}_1\}

is a linearly dependent set.