Prove the following result: Let V be a finite- dimensional vector space, let V1, V2, ..., Vn be vectors in V, and let {1, 2, . ..., n} be a basis for V' with the property that ; (v₂ ) = d¿j for all i, j = 1, 2, . ..., n. Prove that {V₁, V₂, . a basis for V.. Then find an explicit formula for writing an arbitrary u € V as a linear combination of V₁, V2, ..., Vn. ·•·•, Vn} is 9

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A: Here we use the definition of basis and linear combination of vectors as follows

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A: Given : u , v=au1v1+bu1v2+bu2v1+cu2v2 To Prove : Inner product .

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A: Given V is a n- dimensional vector space. Let B be a basis for V. Let B=v1,v2,…,vn. Let u1, u2, …,…

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A: Given: v1, v2, . . . , vn is a basis of vector space V. We have to show that, v1, v1+v2, v1+v2+v3, .…

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Q: 2. Prove that the following vectors |v1) = (1, 1, 0) |v2) = (1, 2, 0) |v3) = (0, 1, 2) span C3. Are…

A: Given that,                    |v1> = 1 , 1 , 0                    |v2> = 1 , 2 , 0…

Q: Compute the norms of the following vectors in R": (a) (1,1, 1,..., 1, 1)

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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A: Vector space, W=span2, 1, 3, 4, 0, 4Vectors : 2, -1, 1 and 3, 2, 7

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Q: Prove the following result: Let V be a finite-dimensional vector space, let V₁, V2, ..., Un be…

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A: 1. Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if S…

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A: “Since you have asked multiple questions, we will solve the first question for you. If youwant any…

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A: Hey, thanx for your question. According to our policy I m answering question first. Please post the…

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Q: Let V and W be vector spaces and let T E L(V, W). (a) Suppose V is finite-dimesnional, m is a finite…

A: let V and W be the vector space and let T∈LV,W (a) suppose V is finite dimensional  implies, dimV=n…

Q: 30. Let S = {v1, V2, . .., V,} be a set of non-zero vectors in a vector space V and W = span S.…

A: See the detailed solution below.

Q: {{: "]ancee}. Let V = Prove that V is a vector space over Q, and find a basis for V over Q.

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A: v={A in M22 : A is upper triangular}

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Q: Show that the vector space P, has the basis S = {1, x, x², x³}. %D

A: We have to solve given problem:

Q: Let {u1, ·.., Un} be a list of vectors in an n-dimensional vector space V and let B be a basis for…

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A: Basis of the vector space

Q: Problem 3. Suppose the vector space V = P3, given the following four polynomials 1+13, 1+t, -t+2t2,…

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