Consider subsets W of a vector space V: (a) V = R³, W = {[x₁, x2, x3] | − 2x1 − 2x2 + x3 = 0}; (b) V = R³, W = {[ab, 3b+ 2a, a - b] | a, b = R}; (c) V = R¹, W = {[X1, X2, X3, X4] | − 2x1 − 2x2 + x3 + x4 = 5}. In each case determine if the given subset W of a vector space V is a subspace. In cases when W is a subspace of V, find a basis and the dimension of W. Justify every step of your answer.

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Q: (a) u, v, w are vectors such that u·v = 3, u·w= -2, v·w= 5. Then, (u+ 2v)· • w = (b) {u, v, w} is a…

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Q: (c) Find the distance between the two points u = (9, -3, 4) and v = (−3, 2, 5). (d) Find the norm of…

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Q: Use the function to find the image of v and the preimage of w. T(v1, v2, v3) = (4v2 - v1, 4v1 +…

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Q: Consider the vectors u₁ = [1,0,-1], u2 = [1,0,0] and u3 = [0, 1,1], v= [5, 1,3] and w= [1,0,3]. (a)…

A: As per guidelines of Bartleby i am supposed to solve on first three part,if you want more solution…

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Q: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

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Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

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Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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Q: What is the dimension of the vector space P°?

A: The dimension of Pn is n+1

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A: u and v are vectors.

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Q: ) The vectors (3,0,0,0), (0,−1,2,1), (6,2,−6,0) and (3,−2,3,3) in ?4 are linearly independent.

A: solve the following

Q: Let A = [[3,1,1,2,2],[-3,-2,4,2,2],[-5,5,4,-1,-2]]  Give a nonzero vector x in the nullspace of A.

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Q: Consider the vector space V defined by V = {(x, y, z) | x+y+z=0}. Let u = (1, -2, 1) and v = (3, -1,…

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Q: Consider the set of vectors B = {(1, 0, 2), (2, 1, -1), (3, 0, 7)} (1) Is 3 linearly independent?…

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Q: Use the function to find the image of v and the preimage of w. T(V₁, V2, V3) = (4V2 V₁, 4v₁ + 5v₂),…

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Q: Check whether the sets of vectors (i) ā = {1, 1, 1}, b = {1, 2, 0} , č = {0, – 1, 2} and (ii) ā =…

A: Hi, thank you for the question. Since you have posted multiple questions, as per our policy we…