Consider the set of vectors )() 1 2 1 S = 2 3 1 -2 (i) Determine if this set of vectors is linearly independent or linearly dependent. (ii) If the set is linearly dependent, determine a linear dependent relationship between these vectors. (iii) Consider the transformation xi + 2x2 + x3 2x1 + 3x2 + x3 + 2 T 13 3x1 + x2 – 2x3 - Determine if T is a linear transformation or not.

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: 2. Describe a linear map which maps the set of vectors (-²2) 0 (6) (2) to the set of vectors

A: Introduction:  As per the guidelines i solves first question. For more solutions please repost the…

Q: 1 4 7 Determine whether the set of vectors 2 3 6 9 is linearly dependent or not. If so, find a way…

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Q: (а) (4, — 1, 2), (-4, 10, 2) (Ъ) (—3,0, 4), (5, — 1, 2), (1, 1, 3) (c) (8, – 1, 3), (4,0, 1)

A: As per rules, we will solve first three subparts: a) Given vectors are   u=4,-1,2, v=-4,10,2. To…

Q: Show that V1, V2, V3 are linearly independent, but V₁, V2, V3, V4 are not. Then express V4 as a…

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Q: Eхample: *-? 3 -", -13 2 2. x, =[4 4 -are Determine if the vectors: linearly dependent or not.…

A: The linear dependency of vectors is solved as follows :

Q: a Let A = b - a then A is diagonalizable. b Select one: O True O False

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Q: Find all values a for which the set {(a — 5, 13, 0), (−1, a – 9,0), (4, 0, a — 2)} is linearly…

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Q: (a) (b) Any set of vectors containing the zero vector is linearly dependent. Any set of more than ʼn…

A: Let  be a sub set of  containing the zero vector               Then consider the following…

Q: 5) Let 0 H 1 0 Can w be written as a linear combination of V1, V2, V3, and v4? V₁ = 2 V₂ = 2 3 1 and…

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Q: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii)…

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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

A: Linearly department vectors

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A: Set of vectors x1, x2, ...xk is independent vectors if for scalar a1, a2,..., an.…

Q: (a) Determine if u̟ and u2 are linearly dependent or independent. (b) Determine if u1, u2 and uz are…

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Q: (a) Determine whether W= (0, 5, 4) can be expressed as a linear combination of the vectors v1 =…

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Q: Determine whether each of the following sets of vectors are linearly dependent or linearly…

A: Kindly refer to Step 2 for the solution.

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: 2. Let -2 and a (a) Check whether u and v are linearly independent or not. (b) Check whether w is a…

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Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

A: According to the given information, it is required to find a linear dependence between the columns…

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: Which of the following operators in R'are linear? 1. T(x) = (8x2, -5x, -9x) %3D 2 T(x) = (10x; - 7x2…

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Q: 3 3. Let V = 5. Find vectors b₁, 62, 63 such that is a linear combination of b₁, b₂, b3. Additional…

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Q: 21 -2 and y -3 3 Express the vector v as a linear combination of a -4 y.

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Q: 1 (a) Is the vector 2 in the span of -1 and 2 ? Justify your answer 3 1 (b) Is the set linearly…

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