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Let V and W be n-dimensional vector spaces, and let T: V * W be a linear transformation
Chapter 2, Problem 15(choose chapter or problem)
QUESTION:
Let V and W be n-dimensional vector spaces, and let T: V * W be a linear transformation. Suppose that 0 is a basis for V. Prove that T is an isomorphism if and only if T(0) is a basis for W.
Questions & Answers
QUESTION:
Let V and W be n-dimensional vector spaces, and let T: V * W be a linear transformation. Suppose that 0 is a basis for V. Prove that T is an isomorphism if and only if T(0) is a basis for W.
ANSWER:Step 1 of 3
Assume that be an isomorphism, where and is an n-dimensional vector space.
Let be a basis for .
Then,
Let