Question

(True or false.) Let V be an n-dimensional vector space, and let S be a k-dimensional subspace of V, where k < n. If {⃗v1,...,⃗vk} is a basis for S and {⃗vk+1,...,⃗vn} is a set of n − k linearly independent vectors not in S, then {⃗v1,...,⃗vk,⃗vk+1,...,⃗vn} is a basis for V.

Answer 1

(True or false.) Let V be an n-dimensional vector space, and let S be a k-dimensional subspace of V, where k < n. If {⃗v1,...,⃗vk} is a basis for S and {⃗vk+1,...,⃗vn} is a set of n − k linearly independent vectors not in S, then {⃗v1,...,⃗vk,⃗vk+1,...,⃗vn} is a basis for V.

Answer 2

sorry