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

Q: 10 -00-0 7 12 5 -8- Are the vectors 6 and linearly independent? Explain! 8

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Q: 7.) for which value(s) of k are the following vectors linearly independent? u =

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Q: Determine if the following set of vectors is LD or LI. If LI explain how you know (explain your…

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

Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

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Q: Given three non-zero vectors, a, b & C, is it possible to evaluate a b Explain with an example. •6•²

A: We have given three non-zero vector.

Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

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Q: 4

A: We are given the following vectors.

Q: What if the vector v was [ 7, 11, 3]

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Q: -0-0-0-0 3 and b (a) Determine if bis a linear combination of a,, a, and a,. (b) Determine if the…

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Q: 8. Consider the vectors [11, 2, 0, 1, 0, 2], [0, 1, 1, 2, 1, 2], [2, 1, 2, 1, 1, 1]); [0, 1, 1, 1,…

A: Remark: If no column (row) of a matrix can be written as linear combination of other columns (rows)…

Q: 6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear…

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Q: 5. Suppose that a, b and care vectors such that |a| = 2, |6| = 1, || = 5, a·b = 0, a. c = 3 and b c…

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: 10. The set of vectors: [0 1-3 -1], (1 01 1] is linearly independent. Answer: yes or no

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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: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

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Q: 1) Determine if the vector b can be written as a linear combination of the vectors a₁, az, and al 1…

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Q: Which of the following is a necessary condition for a set of vectors {V1, V2, ..., Vp} in R" to be…

A: Given that the set of vectors v1, v2,...,vp in ℝn. We have to find the necessary condition for the…

Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

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Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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