3.- Define the vector that allows the linear combination and if it exists, demonstrate the linear combination of the vector w with the set of given vectors: w = (11, -3, 11) S = {(2,-1,3), (1, 2, -1), (3, 1, 1)}

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

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

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Q: 1] Determine whether the first vector is a linear combination of the other vectors. (c) (-1, 15);…

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Q: Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

A: topic - vectors

Q: Express vector t = (3, 6, -6, 9) as a linear combination of vectors u = (-1, 3, 0, 7) and v = (-5,…

A: The given vectors are: t=3, 6, -6, 9u=-1, 3, 0, 7v=-5,0, 6, 5 We have to express the vector t as a…

Q: 123 Write the vector 2 as a linear combination of the vectors 3 4 (6676) 5 4 2

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Q: Determine if the vectors , and are linearly independent.

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Q: Express the vector p = (-6,15,-3) as linear combination of the vectors u = (1,-1,3), v = (2,-5,0)…

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Q: Show that the vectors (1,0,1); (-1,2,3) and (0, 1; -1) spans R³

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Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

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Q: Find a vector perpendicular to (2, −1, 10) and (1, 2, −1)

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Q: f possible express the vector v as a linear combination of 1, V2, and V3. b) v = (0, 0, -1), V₁ =…

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Q: 5) Find a vector in component form that is orthogonal to the vectors a = (9,3,-7) and b = (10,-8,2)

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Q: Express i = (3,7,-4) as a linear combination of i = (1,2,3), ỷ = (2,3,7), z = (3,5,6), also check…

A: see below the answers

Q: If possible express the vector v as a linear combination of V1, V2, and V3. (b) v = (0, 0, -1), V₁ =…

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Q: Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1,-1,2) 14.- Perform…

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Q: If possible express the vector v as a linear combination of V₁, V₂, and V3. =(0, 0, 0), V₁ = (3, -1,…

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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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