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Let T:V → W be a linear transformation, where W is finite dimensional. Note also that rank(T) = dimW. Then, which of the following is correct? a) T is both onto and one-to-one c) T is onto b) T is neither onto and one-to-one d) ker(T) = {0}

Let T:V → W be a linear transformation, where W is finite dimensional. Note also that rank(T) = dimW. Then, which of the following is correct? a) T is both onto and one-to-one c) T is onto b) T is neither onto and one-to-one d) ker(T) = {0}

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.2: The Kernewl And Range Of A Linear Transformation
Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...
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Let T:V → W be a linear transformation, where W is finite dimensional. Note also that rank (T) = dimW. Then, which of the following is correct? b) T is neither onto and one-to-one d) ker (T) = {0} a) T is both onto and one-to-one c) T is onto
Transcribed Image Text:Let T:V → W be a linear transformation, where W is finite dimensional. Note also that rank (T) = dimW. Then, which of the following is correct? b) T is neither onto and one-to-one d) ker (T) = {0} a) T is both onto and one-to-one c) T is onto
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