Determine whether the sets S₁ and S₂ span the same subspace of R³. S₁ = {(1, 2, -1), (0, 1, 1), (2, 5, -1)} S₂ = {(-2, -6, 0), (1, 1, -2)} S₁ and S₂ span the same subspace of R³. O S₁ and S₂ do not span the same subspace of R³.

Q: O Linear subspace L is given by the equations 2r1 + r2 + 3r3 - 14 = 0 = 0 3r1 + 2r2 – 2r4 3r1 + 12 +…

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A: Given,        To  find the closest point to v in the subspace W spanned by

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Q: If the set {(1,2, 1), (0,1, 1), (1, -3, A)} is linearly independent, then (A) A = -4 %3D (B) A + 4…

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A: closure property scalar multiplication satisfied

Q: II. Determine if the set S spans R³. If the set does not span R³, then give a geometric description…

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Q: Section B: Determine of the following set W is subspace of V=R³: W-{(a, 1, 1): a ER).

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Q: True/False: If V is a subspace of R", then dim(V) + dim(V+) = n. True False

A: This is true and follows from a famous theorem in linear algebra.

Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

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Q: Determine whether the sets S, and S2 span the same subspace of R³. s, = {(2, 4, –2), (0, 2, 2), (4,…

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Q: -6 -0-0-0-8 9 6 Let v₁ = -3 4 3 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". 13 9 and w= 6 10 4.…

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Q: 3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

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Q: |412 = -a}, verify that S'is a 7. Let S subspace.

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Q: 14) Find all values of h such that y will be in the subspace of 3 spanned by v1, v2, v3 if vị = 2,…

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Q: If the set {(1, 2, 1), (0, 1, 1), (1,–1, A)} is linearly independent, then (A) A# -2 (B) A # 2 (C) A…

A: The objective is to find the correct option.