Consider the vector subspaces U, V  ,W ⊆ Rn such that U ⊆ V ⊆ W. If dimU = 5 and dimW = 7, what can be said about V? -It always contains a set of 5 linearly independent vectors  -dimV = 6 -it always contains a set of 7 linearly independent vectors  -the zero vector is not contained in it  -it contains a non-zero vector

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 that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Suppose that {x1, x2, x3} is a linearly independent set of vectors in a vector space V . Must {x1,…

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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…

A: The objective of the question is to verify if the vector w is equal to the sum of the vectors V1,…

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: Determine the values(s) of h, if any, for the which the set of vectors {a1.a2,a3} is a linearly…

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Q: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

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Q: The vector w = and V3 = True False 1 -5 0 28 -31 8 31]" in M2x2 vector space is a linear combination…

A: Given that w=0828-31v1=1-210v2=-1308v3=1-4-53

Q: Suppose that three vectors u, v, and w are linearly independent in some vector space. Are the…

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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…

A: Given three vectors which span w.

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

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Q: Determine whether the following set of vectors are linearly independent

A: Step 1: Step 2: Step 3: Step 4:

Q: 3) For each set of vectors below, determine if the set is dependent or in- dependent. If the set is…

A: We will first check the linearly independence of this set of three vectors