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Answer the folowing if it is: ALWAYS TRUE, SOMETIMES TRUE or NEVER TRUE. (a) If S={u,,u,,u,,u} is linearly independent then S spans R³ (b) If A is m x n and rank A = m, then the linear transformation T: x -> Ax is one-to-one. (c) If dim V = dim W then V and W are isomorphic vector spaces.

Answer the folowing if it is: ALWAYS TRUE, SOMETIMES TRUE or NEVER TRUE. (a) If S={u,,u,,u,,u} is linearly independent then S spans R³ (b) If A is m x n and rank A = m, then the linear transformation T: x -> Ax is one-to-one. (c) If dim V = dim W then V and W are isomorphic vector spaces.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 12EQ
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Answer the folowing if it is: ALWAYS TRUE, SOMETIMES TRUE or NEVER TRUE. (a) If S={u,,u,,u,,u} is linearly independent then S spans (b) If A is m x n and rank A = m, then the linear transformation T: x -> Ax is one-to-one. (c) If dim V = dim W then V and W are isomorphic vector spaces.
Transcribed Image Text:Answer the folowing if it is: ALWAYS TRUE, SOMETIMES TRUE or NEVER TRUE. (a) If S={u,,u,,u,,u} is linearly independent then S spans (b) If A is m x n and rank A = m, then the linear transformation T: x -> Ax is one-to-one. (c) If dim V = dim W then V and W are isomorphic vector spaces.
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