Solved: Proof Let {v1, v2, . . . , vk} be a linearly

Chapter 4, Problem 71

(choose chapter or problem)

Let \(\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \ldots, \mathbf{v}_{k}\right\}\) be a linearly independent set of vectors in a vector space V. Delete the vector \(\mathbf{v}_{k}\) from this set and prove that the set \(\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \ldots ., \mathbf{v}_{k-1}\right\}\) cannot span V.

Text Transcription:

{mathbf v_1, mathbf v_2, ldots, mathbf v_k}

mathbf v_k

{mathbf v_1, mathbf v_2, ldots ., mathbf v_k-1}