5. Consider R² with the unusual inner product (x, y) defined by:{(:) (:))=((:) (:))=а- 2ар-аq-bр+2bgFor 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 p of x =onto y =(b) Verify that the difference r = x – p is orthogonal to y.(c) Show that this inner product satisfies all three properties in the definition ofinner product.2[Hint: (x, y) = yT (x.]-12

Answered: Image /qna-images/answer/aad20fca-8c51-4107-bbdd-c01ae00b18f6.jpg

(a) In the geometry of this unusual inner product space (where ||x|| = /{x, x)), find the vector projection p of x = 3 onto y = -7 (b) Verify that the difference r = x – p is orthogonal to y. (c) Show that this inner product satisfies all three properties in the definition of inner product. (Hint: (x, y) = y" ( 2 -1 x.] 1 2

(a) In the geometry of this unusual inner product space (where ||x|| = /{x, x)), find the vector projection p of x = 3 onto y = -7 (b) Verify that the difference r = x – p is orthogonal to y. (c) Show that this inner product satisfies all three properties in the definition of inner product. (Hint: (x, y) = y" ( 2 -1 x.] 1 2

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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