Solution: Exercises 23–26 concern a vector space V, a basis

Chapter 4, Problem 25E

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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,

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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

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