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The following definition is used in Exercises 24 27 and in Exercise 30. Definition. Let

Chapter 2, Problem 24

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QUESTION:

The following definition is used in Exercises 24 27 and in Exercise 30. Definition. Let V be a vector space and Wi and W2 be subspaces of V such that V = W] W2. (Recall the definition of direct sum given in the exercises of Section 1.3.) A function T: V > V is called the projection on Wi along VV2 if, for x = xi 4- x2 with xi Wi and x2 W2, we have T(x) = x\.

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QUESTION:

The following definition is used in Exercises 24 27 and in Exercise 30. Definition. Let V be a vector space and Wi and W2 be subspaces of V such that V = W] W2. (Recall the definition of direct sum given in the exercises of Section 1.3.) A function T: V > V is called the projection on Wi along VV2 if, for x = xi 4- x2 with xi Wi and x2 W2, we have T(x) = x\.

ANSWER:

Step 1 of 2

Let . Since  where , , we will write v with respect to this decomposition, such that . Then by the definition of projection on the y-axis along the x-axis,

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