Consider R2 with the unusual inner product (x, y) defined by: a P (8).(:))= = 2ap-aq-bp+2bq ((G)·()) 3 5 For example, (a) In the geometry of this unusual inner product space (where ||x|| = √(x,x)), find - (1). = 2.1.4-1.5-3.4+2-3-5-8-5-12 +30=21 the vector projection (page 242) p of x = 3 -(-³) -7 -1 (b) Verify that the difference r = x - p is orthogonal to y. (c) [Extra Credit] Show that this inner product satisfies all three properties in the definition of inner product (page 238). 2 [Hint: (x, y) = yT -21 ) -1 x.] onto y =
Consider R2 with the unusual inner product (x, y) defined by: a P (8).(:))= = 2ap-aq-bp+2bq ((G)·()) 3 5 For example, (a) In the geometry of this unusual inner product space (where ||x|| = √(x,x)), find - (1). = 2.1.4-1.5-3.4+2-3-5-8-5-12 +30=21 the vector projection (page 242) p of x = 3 -(-³) -7 -1 (b) Verify that the difference r = x - p is orthogonal to y. (c) [Extra Credit] Show that this inner product satisfies all three properties in the definition of inner product (page 238). 2 [Hint: (x, y) = yT -21 ) -1 x.] onto y =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider R? with the unusual inner product (x, y) defined by:
{(:) (;)).
a
= 2 ap – aq -bp+2bq
((:) (:))
1
4
For example, (
= 2.1.4- 1.5 – 3.4+2.3.5 8- 5 – 12+ 30 = 21
(a) In the geometry of this unusual inner product space (where ||x|| = V (x, x)), find
the vector projection (page 242) p of x =
3
onto y
-7
(b) Verify that the differencer =x - p is orthogonal to y.
(c) [Extra Credit] Show that this inner product satisfies all three properties in the
definition of inner product (page 238).
[Hint: (*,y) = y" () x]
2 -1
x.]
-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7701ebcd-ae79-49a5-aa56-eff1f72328a6%2F4fe08951-8fb3-4346-81f2-d0e198628310%2F9uz146j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider R? with the unusual inner product (x, y) defined by:
{(:) (;)).
a
= 2 ap – aq -bp+2bq
((:) (:))
1
4
For example, (
= 2.1.4- 1.5 – 3.4+2.3.5 8- 5 – 12+ 30 = 21
(a) In the geometry of this unusual inner product space (where ||x|| = V (x, x)), find
the vector projection (page 242) p of x =
3
onto y
-7
(b) Verify that the differencer =x - p is orthogonal to y.
(c) [Extra Credit] Show that this inner product satisfies all three properties in the
definition of inner product (page 238).
[Hint: (*,y) = y" () x]
2 -1
x.]
-1
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