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Solution: Exercises 23–26 concern a vector space V, a basis
Chapter 4, Problem 25E(choose chapter or problem)
Problem 25E
Exercises 23–26 concern a vector space V, a basis and the coordinate mapping
Show that a subset in V is linearly independent if and only if the set of coordinate vectors is linearly independent in . Hint: Since the coordinate mapping is one-to-one, the following equations have the same solutions,
Questions & Answers
QUESTION:
Problem 25E
Exercises 23–26 concern a vector space V, a basis and the coordinate mapping
Show that a subset in V is linearly independent if and only if the set of coordinate vectors is linearly independent in . Hint: Since the coordinate mapping is one-to-one, the following equations have the same solutions,
ANSWER:
Solution 25E
Consider the statement: a subset in is linearly independent if and only if the set of coordinate vectors is linearly independent in.
The coordinate mapping is one-to-one then the followin