Q7. A. Show that (x, y) = 5x1yı-9x2y2 for vectors x (x, x2) and y %3D defines an inner product. C. Let V be P2 with the inner product given by evaluation at -2, -1, 0,1 3t + 2, p2(t) = 2t2 +t and p3(t) = 3t2- 1. Find the orthogonal 1 %3D %3D the subspace spanned by p1 and p2-

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...
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Q7. A. Show that (x, y) = 5x1y1- 9x2y2 for vectors x = (x, x2) and y = (y1, yz) in R2
defines an inner product.
C. Let V be P2 with the inner product given by evaluation at -2, -1, 0, 1 and 2. Let p,(t) =
3t + 2, p2(t) = 2t2
+t and p3(t)= 3t2 -
- 1. Find the orthogonal projection of p3 onto
the subspace spanned by p1 and p2-
W
EN
FUJITSU
Transcribed Image Text:Q7. A. Show that (x, y) = 5x1y1- 9x2y2 for vectors x = (x, x2) and y = (y1, yz) in R2 defines an inner product. C. Let V be P2 with the inner product given by evaluation at -2, -1, 0, 1 and 2. Let p,(t) = 3t + 2, p2(t) = 2t2 +t and p3(t)= 3t2 - - 1. Find the orthogonal projection of p3 onto the subspace spanned by p1 and p2- W EN FUJITSU
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