Let W = Span(v₁, V2, V3) where 1 --0--0--0 1 -1 3 Note that V₁, V2, V3 is an orthogonal basis of W. Let y = 5 4 (a) Find the orthogonal projection of y onto the subspace W. (b) Write y as a sum of a vector in W plus a vector in W+. (c) Find the distance from y to W.

Q: Find the coordinates of the vector v = (7,4) with respect to the basis U₁ = (2, 1) and u₂ = (3,1).

A: The answer is given below:

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Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

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Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

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Q: Find the basis for the orthogonal complement V: v1=(1,-3,3,5) v2=(2,-5,9,3)

A: The given vectors  and .The objective is to find the orthogonal complement of the given vectors.

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Q: Let {u₁, U₂, U3, U4} be the orthogonal basis for R¹ given below. Write x as a sum of two vectors v₁…

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Q: Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy-plane. Let T…

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Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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