Consider the two dimensional subspace U of R³ spanned by the set {₁, 2} where U₁ = 4₁ = U₂ = U3 = 1. -2 2 -2 , 42 = The orthogonal complement V = U¹ of U € R³ is the one dimensional subspace of R³ such that every vector ve V is orthogonal to every vector € U. In other words, u ue U and ve V. Find the first two components ₁ and ₂ of the vector ve V for which v3 = 1. -6 0 v=0 for all

Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: ▶Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, v3)…

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Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

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A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

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A: (a) The given vectors are: v1=(1,2,3,4), v2=(0,1,0,-1), v3=(1,3,3,3)

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Q: 9. Determine whether the vectors v₁ = (1,1,2), v₂ = (1,0,1) and v3 = (2,1,3) span the vector space…

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Q: show that the vectors V₁ = (2,0,- 2, 1) > V₂ = (3,1, -5,0) and V3=(2, 2, -6, -2) form Linearly…

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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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