线性代数证明题（英文） 求高手！！！

线性代数证明题（英文） 求高手！！！
Let T : Rm → Rn be a linear transformation.
(1) Prove that T is injective if and only if for every linearly independent set {v1, . . . ,vk} in Rm, the
set {T(v1), . . . , T(vk)} is linearly independent in Rn.
(2) Prove that T is surjective if and only if for every set of vectors {v1, . . . ,vk} that span Rm, the set {T(v1), . . . , T(vk)} spans Rn.
(3) Use parts (1) and (2) to fill in each blank with 4 words or less, and prove the statement: T is invertible if and only if for every set of vectors {v1, . . . ,vk} ——（填空）that Rm, the set{T(v1), . . . , T(vk)} also——（填空） Rn.
求证明过程，中英文皆可！！！