Explanation Given: T : V → W be a linear transformation B and C be ordered bases for V and W . Approach: Let w belongs to Rng ( T ) . w is written as, w = T ( v ) for some v in V [ w ] C = [ T ( v ) ] C for some v in V [ w ] C = [ T ] B C [ v ] B for some v in V So, right hand side of the final statement is expressed as linear combination of the columns of [ T ] B C

Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)

4th Edition

ISBN: 9780321985811

Author: Stephen W. Goode, Scott A. Annin

Publisher: Pearson (edition 4)

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Chapter 6.5, Problem 21P

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To prove:

For all w in W, W belongs to Rng(T) if only if [w]C belongs to colspace([T]BC)

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Chapter 6.5, Problem 20P

Chapter 6.6, Problem 1AP

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Chapter 6 Solutions

Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)

Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - For problem 1-8, verify directly from Definition...Ch. 6.1 - For problems 1-8, verify directly from Definition...Ch. 6.1 - For problem 1-8, verify directly from Definition...Ch. 6.1 - For problem 1-8, verify directly from Definition...

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To prove: For all w in W , W belongs to Rng ( T ) if only if [ w ] C belongs to colspace ( [ T ] B C )

Solution Summary: The author proves that for all w in W, it belongs to Rng(T).

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To prove:

For all w in W, W belongs to Rng(T) if only if [w]C belongs to colspace([T]BC)

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Chapter 6 Solutions

To prove: For all w in W , W belongs to Rng ( T ) if only if [ w ] C belongs to colspace ( [ T ] B C )

Solution Summary: The author proves that for all w in W, it belongs to Rng(T).

Videos

To prove: For all w in W, W belongs to Rng(T) if only if [w]C belongs to colspace([T]BC)

Want to see the full answer?

Chapter 6 Solutions

To prove:

For all w in W, W belongs to Rng(T) if only if [w]C belongs to colspace([T]BC)