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Given set of vectors [1] = 0, v, = 2, v, =1 in R' 2 a) Make the vectors v,,v; in to an orthonormalized set w,, w; b) Find the orthogonal projection of v, onto the plane spanned by w,, w, [1] [1] V c) Find the component of v, orthogonal to the plane spanned by w,, W -

Given set of vectors [1] = 0, v, = 2, v, =1 in R' 2 a) Make the vectors v,,v; in to an orthonormalized set w,, w; b) Find the orthogonal projection of v, onto the plane spanned by w,, w, [1] [1] V c) Find the component of v, orthogonal to the plane spanned by w,, W -

Advanced Engineering Mathematics
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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Please do all the parts of the question especially C

Given set of vectors [1] v, = 0, v, = 2. V3 in R a) Make the vectors v,,v; in to an orthonormalized set w,, w; b) Find the orthogonal projection of v, onto the plane spanned by w,, w, c) Find the component of v, orthogonal to the plane spanned by w,, w; - Confirm that the unit vectors w, =- is orthogonal to the plane and together with w. w, make it an orthonormal set {w, , w,. w;} for {v,,v,,v;}
Transcribed Image Text:Given set of vectors [1] v, = 0, v, = 2. V3 in R a) Make the vectors v,,v; in to an orthonormalized set w,, w; b) Find the orthogonal projection of v, onto the plane spanned by w,, w, c) Find the component of v, orthogonal to the plane spanned by w,, w; - Confirm that the unit vectors w, =- is orthogonal to the plane and together with w. w, make it an orthonormal set {w, , w,. w;} for {v,,v,,v;}
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