subspace spanned by < x,y >= X₁Y₁X₁Y2X2V₁ + 4X2Y2, and let P be the orthogonal projection of R² onto W. Find 3,4). Suppos x = (x₁, x₂), y = (V₁, V2) the matrix of P relative to standard basis i) Wt i) an orthonormal basis in which P is represented by the matrix [] ed as
subspace spanned by < x,y >= X₁Y₁X₁Y2X2V₁ + 4X2Y2, and let P be the orthogonal projection of R² onto W. Find 3,4). Suppos x = (x₁, x₂), y = (V₁, V2) the matrix of P relative to standard basis i) Wt i) an orthonormal basis in which P is represented by the matrix [] ed as
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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![Let W be the subspace of R² spanned by the vector (3,4). Suppose the inner product is defined as
x = (x₁, x₂), y = (y₁, y₂)
< x,y >= X₁Y₁X1Y2X₂Y₁ + 4X2Y2,
and let P be the orthogonal projection of R² onto W. Find
i) the matrix of P relative to standard basis
ii) W¹
iii) an orthonormal basis in which P is represented by the matrix []](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18306282-f933-4068-a09a-779164b2089a%2F48786645-99c0-4849-8719-cba1468f6f85%2F4rtaec_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let W be the subspace of R² spanned by the vector (3,4). Suppose the inner product is defined as
x = (x₁, x₂), y = (y₁, y₂)
< x,y >= X₁Y₁X1Y2X₂Y₁ + 4X2Y2,
and let P be the orthogonal projection of R² onto W. Find
i) the matrix of P relative to standard basis
ii) W¹
iii) an orthonormal basis in which P is represented by the matrix []
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