Test the linear independence of a) v1=<1,3,5> v2=<2,1,6> v3=<3,4,11> b) u1=<2,1,6> u2=<3,1,7> u3=<5,2,3> Express v3/u3 as linear combination of v1,v2 / u1,u2 when they are linearly dependent otherwise express x=<1,1,1> as linear combination of the given vectors,

Q: Test the linear independence of a) v1= v2= v3= b) u1= u2= u3= Express v3/u3 as linear combination…

A: The given vectors are a) v1=1, 3, 5v2=2, 1, 6v3=5, 2, 3 b) u1=2, 1, 6u2=3, 1, 7u3=5, 2, 3 We have to…

Q: Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent.

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Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

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Q: (Section 5.3) i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and v3 = (1,3,3,3)…

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Q: A make linearly dependent set of vectors in R^4 Plase make sure you list three different reason why…

A: There are three different reasons why the set of vectors in R^4 is linearly dependent. If a set…

Q: 3- The vectors x, = R3, are linearly independent. (1,0,1), x2 = (-1,0,1) and x3 = (-2,4, –3) in O…

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Q: {(1, 2, 3),(3, 2, 1),(0, 0, 1)}. Show that B is linearly independent and spans R3.

A: Linear span: Let V represent a vector space, and S=(v1,v2,...,vn) represent a subset of V. If every…

Q: Find the least-squares line y = Bo + B1x that best fits the points (-3, -4), (-1, 1), (1,5), (3, 8)

A: Use least square method to solve it

Q: 18 as a linear combination of a and y Express the vector v y.

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Q: Find the stable vector of 1 3 4 4 P = 4 %3D 3 7

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

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Q: Determine whether the vectors v₁ = (1, 6, 0, 0), v₂ = (0, -1, 0, 1), v3 = (0, 0, 1, 1), and v₁ = (1,…

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Q: Let ui = (3, –1,3, 3), u2 = (-2,3, 1, 3), and uz = (0, –1, -1, –1). Write v = (8, –9, 1, –1) as a…

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Q: 5. Let u= w= [-]-[], and w (a) Show that w is not a linear combination of u. (b) Show that u and V…

A: We have to show that-w is not a linear combination of u,u and v are linearly independent,w is a…

Q: Write v (2,5, –4,0) as a linear combination of uz = (1,3,2, 1); U2 (2, — 2, -5,4); из %3D (2,…

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Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: 9. Explain why four vectors is R³ are always linearly dependent.

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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: Can we write v = (1,5,4) as a linear combination of u = (1,3, -2), uz = (2,7,-1), ug = (1,6,7) ?

A: If there exist a,b,c∈ℝ such that au1+bu2+cu3=v then we can say  v as a linear combination of u1,u2…

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

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Q: Test the linear independence of b) u1= u2= u3=<5,2,3

A: The given vectors are u1=2, 1, 6u2=3, 1, 7u3=5, 2, 3 We have to test the linear independence of…

Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

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Q: Test the linear independence of a) v1= v2= v3=<3,4,1

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Q: Let A = (5,-7,6), B = (2,1,3) and C = (2,-37,-3). a) Find whether vectors A, B and C are linearly…

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Q: Show that the set S= {(20, 34), (40, 68)} is linearly independent or not?

A: Given set is S= {(20, 34), (40, 68)}

Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

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Q: Q1. Which equation can show the "linearity" of Ordinary Least Square (OLS) assumption? A) Y=B1 +…

A: A linear regression equation only sums the terms in the model while the model must be linear in the…

Q: 5. Determine if the vectors x² + x, 2x²,2x − 3, 9 in P3 are linearly independent or linearly…

A: In this question, we will check the given vectors is linearly independent or dependent.