请教：关于以下线性代数的英文讲的是线性代数的那部分？

请教：关于以下线性代数的英文讲的是线性代数的那部分？
If T:V→W is one-to-one , and{Tv1,…,Tvn} is a basis for W,then {v1,…,vn} is a basis for V
Suppose that V and W are vector spaces, and let T: V→W be a linear trasformation.
Let U be a subspace of W. Show that
Tˉ¹(U):= {v∈V:T(v) ∈}
Is a subspace of V. Explain why this shows that the null space N(T) is also a supace.

能给一下提示吗？（解）此类题的思考点，解题窍门！（我不太懂英文）