Suppose ....,V4}is a linearly dependent spanning set for a vector space V. Show that each w in V can be expressed in more than one way as a linear combination of V4. [Hint: Let w = k¡v1 + •…+ k4v4 /1, . . . , V4 V1, ..., be an arbitrary vector in V. Use the linear dependence of {V1,..., V4 to produce another representation of w , V4.] as a linear combination of V1,,...

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A: You have put multiple questions without any numbering. So, according to the guidelines, we solve…

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A: Linearly dependent

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A: Here, 3 vectors are: {(1,2,3),(4,5,6),(2,1,0)}

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: 4. Determine whether M22 = { 1: a, be R} : a, be R M22 is not a vector space

A: Check vector addition

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A: The given vectors are

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Q: A student learning about linear independence makes the following inaccurate statement: "A subset S…

A: We have to solve given problem:

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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: 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

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

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Q: Use MATLAB to determine whether v is a linear combination of the members of set S. If it is, express…

A: Solution An element v is said to be a linear combination of elements of S if there exists elements…

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A: Please check the next step for details

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Q: Suppose ₁, 2, 3 is an orthogonal set of vectors in R³. Let w be a vector in Span(V₁, V2, V3) such…

A: Given: v1, v2, v3 is an orthogonal set of vectors in ℝ5.           v1·v1=30, v2·v2=25.25, v3·v3=9…

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Q: 13) Check whether the following set of vectors are linearly dependent: ủ1 = (1,2,3), ủz = (1,0,1) ,…

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Q: Consider a set of vectors S = {V₁, V2, V3} following statements is true? = {··]} Which one of the

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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

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A: The objective of this question is to determine whether the set of vectors S = {u1, u2, u3} spans the…

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Q: 1) Suppose v1, V2, V3, V4 span a vector space V. Prove that the list vi - v2, V2 – V3, V3 – V4, V4…

A: Spanning set of the vector space

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Q: 1.W.4 We'll work inside the vector space of polynomials in degree < 2, which is denoted P<2. Let P1…

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