An inner product and an associated norm are defined on R² by the weighted scalar product where u = (2) and v = (u, v) 2u1v1 + 3u₂ v₂ = Let a = (²) and b = (a) Calculate (a, b), (a, a) and ||a|| (aa) b (b) Calculate the vector ca- (a,b) (c) Verify that, with respect to this inner product, the vector c is orthogonal to the vector a, but c is not orthogonal to the vector b

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: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

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Q: Consider the matrix attatched and the vector u = (2 0)*. Let B=(A−AT)2 and define vector v = Bu. If…

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Q: Show that v, = (1,0,–1) , v, = (1,0,1) , v3 = (1,1,1) span R’. %3D Express vector v= (4,2, 2) as…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let u = (-1,0,1), v= (3,2,1) and w= (0,1,2). (b) Prove that the vectors u v and w are linearly…

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Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

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Q: Let u = (2, 1, -2), v= (0,3,-5), and w = Compute the indicated vectors. (a) u × v = (?, ?, ?) (b) -…

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Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: Show that VI = (1,0,1) , v, = (1,1,0) , v3 = (1,1,1) span R'. Express vector v= (2, 1, 3) as linear…

A: v1 ,v2 ,v3 ,...,vn span R^n if det(v1,v2,...,vn) is non zero

Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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