The following statement is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If the statement is true, give a justification. If V₁, V₂, V3 are in R³ and V is not a linear combination of V₁, V₂, then {V₁, V₂, V3} is linearly independent. Fill in the blanks below. The statement is + V₂ = 2 2 false/true Take v, and v₂ to be multiples of one vector and take v. to be not a multiple of that vector. For example, V₂ = 0 Since at least one of the vectors is a linear combination of the other two, the three vectors are linearly -deget/Indecent

Q: Let the set {v,, v2} be linearly dependent. Determine whether the set {v, + 4v,, 5v, - v2} is also…

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Q: Determine which of the following sets are linearly independent. V = -3 -2 5 -6 7 V and U U only V…

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Q: If -2 2 4 V= 3 ,W = 1 4 3 1 2 Is b has linear combination with u, v, and w. If yes, find that…

A: The given vectors,The aim is to check the vector  has a linear combination with  and .

Q: The statement is either true in all cases or false. If false, construct a specific example to show…

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Q: The statement is either true in all cases or false. If false, construct a specific example to show…

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Q: Given V1 = %3D

A: Given,         v1=123, v2=2-1-1, v3=31c

Q: Consider the set S = {2x² + 1, 2x – 4, 2x + x}. The set S spans P2. If t(a) — 6а? + 6х — 15 € Ра,…

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Q: 1. Show that {1,x+1, x² + x+ 1, x³ + x² +x+ 1, x4 + x³ +x² + x+1} is linearly independent in Ps but…

A: Please find the details in next step

Q: Q3) Determine whether the following set is linearly independent. (0,3, –3, –6), (–2,0,0, -6), (0,–4,…

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Q: 1. (a) Find an example of a set of vectors in R³ that is linearly independent but does not span R°.…

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Q: are linearly independent if and only if k # -0-2-0 v= -6 -1 + k 3 = 5 1 1 7

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Q: If |B| = 5, then B spans R4     If |B| = 5, then B is not linearly independent.     If B is a…

A: There are 5 statement. We can either prove or disprove by counter example in each case.

Q: The vectors are linearly independent if and only if k # 3 ·020 v= -3 -16+ k u= 7 22 W =

A: We know that if the vectors are linearly independent then their determinant is not 0. So,…

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Q: Let a1 0,a22, as a3 2, and b = Write b as a linear combination of a₁, a2, and a3, if possible. b= -1…

A: AssumeThe augmented matrix

Q: Which of the following sets is linearly independent? O M={(1,0,1),(3,0,3), (0, 0, 0) } O M={…

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Q: 9.2 If possible, find two vectors ū and v so that (a) a and c are non-negative linear combinations…

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Q: Let u = , v = and w = . Now, i = is a linear combination of ü, v and w. That is, i = aju + azv +…

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Q: For what value of h is the following set linearly dependent? S = {2x +2, 2x² + 4x - 7, 2x² - 10x +…

A: According to the given data, find the value of h:

Q: Determine if the set is linearly independent. S = {(4,0,1), (0, -3,2), (5,10,0)}

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Q: For which values of C is the set C linearly dependent? 3. C = -1, 2 C=-1,-2 C=1,-2 C= - 1, 1 O c=1,…

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Q: The following vectors 3 X= 2 2 12 +b 2 are linearly independent if and only if b

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Q: The product Ax is a linear combination of the columns of.A. The equations.Ax = b have a solution…

A: The product Ax is a linear combination of columns of A. The equation Ax = b have a solution vector x…