Let V be a general vector space and u, v € V be linearly independent. (a) Show that the vectors x = a₁u+a₂v and y = azu+α4v with α; € R are linearly independent if and only if a1a4-a2030. (b) For the case α₁04-a2030, are the vectors {u, v, x, y} linearly independent?

Q: show that the vectors: 2,3), II

A: To prove that the vectors:     v1=(1, 2, 3), v2=(-2, 1, 1), and v3=8, 6, 10 in ℝ3  are linear…

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A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: Let V₁, V2, V3 be linearly independent vectors in R". Show that {v₁ + V₂, V₂ + V3, V3 + ₁} is also…

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Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

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

Q: Find two linearly independent vectors perpendicular to the vector 2 -5 -9 D =

A: Two vectors are said to be perpendicular to each other if and only if their dot product is zero.

Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: Consider the set of vectors B = {(1, 0, 2), (2, 1, -1), (3, 0, 7)} (1) Is 3 linearly independent?…

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Q: Check whether the sets of vectors (i) ā = {1, 1, 1}, b = {1, 2, 0} , č = {0, – 1, 2} and (ii) ā =…

A: Hi, thank you for the question. Since you have posted multiple questions, as per our policy we…

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: If possible express the vector v as a linear combination of V1, V2, and V3.

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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: A2. Express v = (1,-2,5) in R as a linear combination of the vectors u; (1, 1, 1), %3D uz = (1,2, 3)…

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Q: Let v1 = , v2 = , w = vectors ∈ R2. Does the set {v1, v2} span R2?

A: given a set of vectors v1 = <0, 1>, v2 = <-1, 0>we need to find that does the set {v1,…