A First Course in Linear Algebra · Problem LI.T20

Vectors — Robert Beezer

Mathematics — Linear Algebra · linear-independence-proofs

Problem

Suppose that

\{\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4\}

is a linearly independent set in

\mathbb{C}^{35}

. Prove that

\{\mathbf{v}_1,\ \mathbf{v}_1 + \mathbf{v}_2,\ \mathbf{v}_1 + \mathbf{v}_2 + \mathbf{v}_3,\ \mathbf{v}_1 + \mathbf{v}_2 + \mathbf{v}_3 + \mathbf{v}_4\}

is a linearly independent set.