c 19. In each of the following parts, find the orthogonal projection of thegiven vector on the given subspace W of the inner product space V.(a) VR², u = (2,6), and W = {(x, y): y = 4x}.=(b) V = R³, u = (2, 1,3), and W = {(x, y, z): x + 3y - 2z = 0}.(c) V = P(R) with the inner product (f(x), g(x)) = få¹ƒ(t)g(t) dt,h(x) = 4+3x - 2x², and W = P₁(R).

### Part (a)Given: V = R^2, u = (2, 6), and W = { (x, y) | y = 4x }.A basis for W can be v = (1, 4).…

Answered: 19. In each of the following parts,…

Elementary Linear Algebra (MindTap Course List)

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Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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Question

19. In each of the following parts, find the orthogonal projection of the
given vector on the given subspace W of the inner product space V.
(a) VR², u = (2,6), and W = {(x, y): y = 4x}.
=
(b) V = R³, u = (2, 1,3), and W = {(x, y, z): x + 3y - 2z = 0}.
(c) V = P(R) with the inner product (f(x), g(x)) = få¹ƒ(t)g(t) dt,
h(x) = 4+3x - 2x², and W = P₁(R).

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