Exercises 23–26 concern a vector space V, a basis and the

Chapter 4, Problem 23E

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QUESTION:

Exercises 23–26 concern a vector space V, a basis and the coordinate mapping Show that the coordinate mapping is one-to-one. (Hint: Suppose for some u and w in V, and show that u = w.)

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QUESTION:

Exercises 23–26 concern a vector space V, a basis and the coordinate mapping Show that the coordinate mapping is one-to-one. (Hint: Suppose for some u and w in V, and show that u = w.)

ANSWER:

Solution 23EStep 1 Let V be a vector space and supposes that be the basis of the vector space and is in . The coordinates of relative to the basis are the weights such that If are the coordinates of , then the vector in Is the coordinate vector of relative to .The mapping is the coordinate mapping (determined by ).Its need to show that the coordinate mapping is one-to-one

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