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Math / Linear Algebra with Applications 9 / Chapter 5.5 / Problem 34

Linear Algebra with Applications | 9th Edition | ISBN: 9780321962218 | Authors: Steven J. Leon

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Solved: Let x be an element of the inner product space V in Exercise 33, and let p1 and

Chapter 5, Problem 34

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QUESTION:

Let x be an element of the inner product space V in Exercise 33, and let p1 and p2 be the projections of x onto S1 and S2, respectively. Show that (a) x = p1 + p2. (b) if x S 1 , then p1 = 0 and hence S 1 = S2.

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QUESTION:

Let x be an element of the inner product space V in Exercise 33, and let p1 and p2 be the projections of x onto S1 and S2, respectively. Show that (a) x = p1 + p2. (b) if x S 1 , then p1 = 0 and hence S 1 = S2.

ANSWER:

Step 1 of 3

Given data:

Let x be an element of the inner product space V.

Let and be the projections of x onto and respectively.

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