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The following definition is used in Exercises 24 27 and in Exercise 30. Definition. Let
Chapter 2, Problem 24(choose chapter or problem)
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\.
Questions & Answers
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,