Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2 +...+ anvn and also x= b1v1 + b2v2 +...+ bnvn where at least one bi≠ai Explain why this means 0=c1v1+c2v2+...+cnvn for some ci, where at least one ci≠0

Q: 5. Show that if each of the vectors {Bo, B1,...,B,} is a linear combination of {a1,a2,...,a,}, then…

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Q: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

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Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

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Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

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Q: 4. Find the largest possible number of independent vectors among V1 =, v2 = , v3 = , v4 =, v5 =, v6…

A: We have the vectors: v1=1,-1,0,0v2=1,0,-1,0v3=1,0,0,-1v4=10,1,-1,0v5=10,1,0,-1v6=0,0,1,-1 We need to…

Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

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Q: 7. "Let &, n, ở be real numbers and consider vectors (1,5,8²); (1,n,n²); (1,0,0²). Determine the…

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Q: Find a vector v satisfying 3v + (5, 20) = (11, 17).

A: To find a vector v satisfying 3v+(5,20)=(11,17).

Q: Q2: For the vector x=[1,5,7,9,13,20,6,7,8] replace the first five elements of vector x with its…

A: For the vector x = [1,5,7,9,13,20,6,7,8] the maximum of all co-ordinates is, 20 & the minimum of…

Q: A set of 5 vectors in R6 cannot be linearly independent. True False

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Q: Suppose vị and v2 are vectors with |v1| = 2, |v2l = 3, and vị · v2 = 5. Let v3 = proj,, v2, V4 =…

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Q: 8. Suppose v1 is a vector of all entries 1 in R"¹ space, which we call "1-vector". What is ||v1||2…

A: Given that, Suppose v1 is a vector of all entries 1 in ℝn space, which we call 1-vector. What is…

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {1 + 3x…

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Q: Consider the set of vectors S = {2 – x + 4x², 3 + 6x + 2x², 2 + 10x – 4x²} in P2. Show that the set…

A: use linear independent vector definition

Q: If x ER" is an n x 1 column vector, then ||x||- Select one: O True O False xx", where x is the 1 x n…

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Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. S = {1 +…

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Q: 9. Show that is a two-dimensional vector. Ai = -x2 X1

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Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {7 − 4x…

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Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩.Express y as the sum of two vectors: one parallel to x, the other…

A: Given that: x=(1,1,1) and y=(0,3, -2) are two  vectors. Let us say,  w = (a, b, c ) is a vector…

Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

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Q: determine if the vector v is a linear combi­nation of th e remaining vectors.

A: To determine: Find if v is linear combination of remaining vectors

Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: Show that if R" = Span(v1, v2, · .· Vk) for some vectors v; of R" with k > n then one can find n…

A: Given:           If            ℝn = Span(v1,v2,..........vk) for vi of ℝn  with k>n, Prove:…

Q: Give examples of two sets of vectors in P3 such that one of them is linearly independent and another…

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Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

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Q: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: Show that there are no vectors u and v such that llull = 1, llvll = 2,and u·v= 3.

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Q: 1 Let u1 = 3 U2 = -1 , Uz = ,X = then write x as sum of two vectors -3 3 on in span {u1} and other…

A: Given, u1=1101 u2=-13-1-2 u3 = 101-1 x=1-1-33

Q: Let v1, v2, vz be the vectors in R defined by 30 -17 7 -3 v2 15 V3 = -14 -12 -14 18

A: Solution is given below:

Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…

Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

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Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: 5. : Find the largest possible number of independent vectors among 1 Vị V3 -1 Find any independent…

A: We need to find independent vector among above given vectors. We use the row reduced Echelon form to…

Q: prove that 12 div A; = √√√x² {√8 8¹k Ax} = dxr div A¹, where A; and Ai are the covariant and…

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Q: 7) Find all vectors v in F such that 2v + ) -)

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Q: Find Vector production of b onto a  a=(-3,4) b =(6,7)

A: Given data: The first vector is a=(-3, 4). The second vector is b=(6, 7). The dot product of b and a…

Q: 2- We can write the vector x = (19,–1, -) in R³ as a linear combination of the vectors x1 =…

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Q: ): If U, U₁, U₂ are 3 vectors in a vector space V such that 13v₁ = v + 7v₂. Then, u belongs to…

A: It is provided that v, v1, v2 are three vectors in the vector space: V and 13v1=v+7v2. We need to…

Q: 6. Check whether Or not F= (Osxi+CysınztSinz)i is a Coservative vector - fieid

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Q: There are 6 linearly independent vectors in R°. O True False

A: We know that the dimension of the vector space R5 is 5.

Q: There exist an example of 5 vectors in R4 that are linearly independent. O True O False

A: Flase Since dimension of R4 is 4 , every linearly independent subset of R4 contains at most 4…

Q: Suppose that u and v are two vectors with u 1, |v| = 2 and u·v = -1. a. Compute |u +v]. b. Compute…

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Q: 7) Three different vectors in R2 that have a norm equal to 5 are:

A: In the given question we have to find three different vectors in ℝ2 that have norm equal to 5.

Q: S is a linearly independent set,then for any x element of , x is not the linear combination of other…

A: Since, using the following definition of linearly dependent of sets-If a set of vectors is linearly…

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {2 +…

A: Linearly dependent: Let S be a linear space. A set of vectors v1,v2,...vn ∈S is said to be linearly…

Q: If u, v, and w are vectors in R° , where u is non zero and u X v = u X w, then v = w. Select one:…

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Q: 1. Under what conditions will a set consisting of a single vector be linearly independent?

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