(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

the given vectorvand subspace W.

(a)

Let W be the subspace with basis {(1 1 0 1)^{T},(0 1 1 0)^{T},(-1 0 0 1)^{T}} andv=(2 1 4 0)^{T}.

2. Relevant equations

Proj_{W}v= (<W,v> / <W, W>) * W

3. The attempt at a solution

So I'm trying to wrap my head around this problem by imaging a simpler setup, say,v=(2 1)^{T}and W = span{(1 0)^{T},(0 1)^{T}}. Visually I see a plane in R^{2}with the vector(2 1)^{T}sticking out and then any other vector in R^{2}projected upon it. As for the formula for projection, I'm not sure how I can input a subspace W, an infinite set of vectors. What's up with that? Where do I go?

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# Find the projection of W onto v for

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