3.Let T : Rn → Rm be a linear map. Prove that the following are equivalent: a) T is injective. b) For all vectors v1, v2
Posted: Wed Jul 06, 2022 11:46 am
3.Let T : Rn → Rm be a linear map. Prove that the following areequivalent:a) T is injective.b) For all vectors v1, v2, . . . , vk ∈ Rn, if the set { v1, v2, .. . , vk} ⊆ Rn is linearly independent, then the corresponding set{T ( v1), T ( v2), . . . , T ( vk)} ⊆ Rm is also linearlyindependent.