Answer to Question #274212 in Linear Algebra for Dhruv bartwal

Question

If T: U to V is a one- one linear transformation between finite- dimensional vector space V and W , then T is invertible. True or false with full explanation

Answer 1

T is said to be invertible if there is a linear transformation S:W→V such that S(T(x))=x for all x∈V. S is called the inverse of T. In casual terms, S undoes whatever T does to an input x. In fact, under the assumptions at the beginning, T is invertible if and only if T is bijective (one- one and and onto)

Answer: false