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3 Suppose V is finite-dimensional and TE L(V). Prove that the following are equivalent. (a) T is invertible. n (b) Tv₁,..., Tv is a basis of V for every basis v₁, Un of V. n (c) Tv₁, ..., Tv is a basis of V for some basis v₁, , Un of V.

3 Suppose V is finite-dimensional and TE L(V). Prove that the following are equivalent. (a) T is invertible. n (b) Tv₁,..., Tv is a basis of V for every basis v₁, Un of V. n (c) Tv₁, ..., Tv is a basis of V for some basis v₁, , Un of V.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 22EQ
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3 Suppose V is finite-dimensional and TE L(V). Prove that the following are equivalent. (a) T is invertible. n (b) Tv₁,..., Tv is a basis of V for every basis v₁, Un of V. n (c) Tv₁, ..., Tv is a basis of V for some basis v₁, , Un of V.
Transcribed Image Text:3 Suppose V is finite-dimensional and TE L(V). Prove that the following are equivalent. (a) T is invertible. n (b) Tv₁,..., Tv is a basis of V for every basis v₁, Un of V. n (c) Tv₁, ..., Tv is a basis of V for some basis v₁, , Un of V.
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