Consider the R-vector space V=R². Which of the following subsets of V is a subspace? The line 2x+y=1 The line y = 2x O The circle x²+y2=1 The set {(x,y) x ≥ 0 and y ≥ 0}

Q: Consider the R-vector space V-R2. Which of the following subsets of V is a subspace? The line 2x+y=1…

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Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

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A: Vector space

Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

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Q: Let V be set of all polynomials p(x) = ao + a₁x + a²x² + • anx" for which -5 is a root. Mark the…

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Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

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A: Given V = -aa0, -b0b | a, b ∈ℝ

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A: we have to show that the set is linearly dependent by finding a nontrivial linear combination of…

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Q: Determine whether U is a subspace of R³. U = {(2r, –s²,t)lr,s, and t E R}

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Q: Which of the following sets is always linearly dependent? A set that contains the zero vector A set…

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

Q: 1. Let "W" be the set of vectors of the form below. Show that "W" is a subspace of R4. You must show…

A: To show whether W is the subspace or not.

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Q: 6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear…

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Q: (2) Let vị = ( 2 = (2),v3 1 of the vector space R³. (2a) Does the vector v = (6 belong to…

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Q: Show how v is orthogonal to any linear combination formed by w1 and w2

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Q: Describe the zero vector (the additive identity) of the vector space. P3 x + ]+² +

A: We have to describe the zero vector (the additive identity ) of the vector space P3.