In the vector space R the vectors a = (1,0,0,-1), 5= (1,0,1,2), y = (1,0, 8, 1) are given. (a) Is {a, 3,y} linearly independent? (b) Find an orthogonal basis for the subspace W = with respect to the standard inner product. (c) Find the orthogonal projection of the vector (1, 1, 1, 1) onto the sub- space 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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A: Given,   {(x,y,z) ∈ R3:(x,y,z)-(1,1,1)=0}={(x,y,z) ∈ R³:x+y+z=0}=L(1,-1,0),(1,0,-1)} and we need to…

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A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

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Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 0, 1),…

A: Solution is given below