Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, -1, 3), (5, 0, 4)} (a) z = (-1, -2, 2) z = (b) v-(16, - ) 59 V = 4 4 v = ])- (c) w = (2, -6, 10) w = (d) u = (6, 1, –1) u =

Q: Consider A = ⟨0, 4, 2⟩, B = ⟨6, −1, 0⟩ and C = ⟨3, 0, 1⟩. draw the vectors A, B, and C in…

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Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

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Q: What is the component form of the vector with an initial point of (-2, 5) and a terminal point of…

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Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2),(1,-1,-4,0) and (2,1,1,6) vectors in R^4 are…

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Q: Let w= (-1,4,15), v = (1, 2, 8), v = (3, 0,1). Does w belong to span(v,,v,)? If yes, then write the…

A: We will find out the required solution.

Q: Find the vector PP, 1. Р.(3,2) P, (5,7) 2. P(-2,-1) 3. Р (3,3) P,(4,-5) P, (5,5) 2

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: What is the component form of the position vector for a vector with an initial point of (-1,0) and a…

A: We have to find component form of position vector.

Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane

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Q: 8. Write the vector (5,6,0) as a linear combination of the vectors (-1,2,0), (3,1,2), (4,–1,0) and…

A: We have to write the vector (5, 6, 0) as a linear combination of the vectors (-1, 2, 0) , (3, 1, 2),…

Q: Determine whether the set of vectors is linearly independent: {(1,0,1), (3,4,-3), (2,2,-1)}.

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Q: Let v1 = [1, 1, 0, 2], v2 = [0, 1, 2, 3], v3 = [-1, 0, 2, 1), V4 = [ 3, 1, -4, 0] and b = [4, 3, -2,…

A: Given

Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: Find a vector a that has the same direction as (-8, 5, 8) but has length 3. Answer: a =

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Q: Which of the following vectors is the scalar multiple of z-(4, 3, -2) ? Ou- (-28, -21, -14) Ou-(-24,…

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Q: Express the vector of the form v=vi+ v2j + v3k. AB if A is point (-9, -2, 1) and B is point (-4, -9,…

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Q: (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1,…

A: We have to check

Q: 1. Find the resultant of the vectors A and B. A = 8a, + 7a, + 2a, В - - За, — 8а, - ба, Draw the…

A: Given that: A→=8ax+7ay+2azB→=-3ax-8ay-6az

Q: Express the vector in the form v = V¡i + v2j + v3k. P2 if P1 is the point (4, -5, 6) and P2 is the…

A: Given :                      P1 4,-5,6 and P2 6,-8,2

Q: Determine if the vectors , and are linearly independent.

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Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

A: a) Given:     w=1,1,5, v1=7,7,7      v2=2,5,3, v3=4,1,-1 w=i^+j^+5k^, v1=7i^+7j^+7k^…

Q: 2) Determine whether the (7, 9, 15) vector is a linear combination of the (1,1 ,2 ),( 1,2,1 ).( 2,3…

A: see 2nd and 3rd step.

Q: Let v,,v,.v be vectors. Show that at least one of the vectors can be written as a linear…

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Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: Express the vector in the form v = vji + v2j + v3k. AB if A is the point (-9, -5, 5) and B is the…

A: A-9,-5,5 and B-4,-12,8

Q: Find four different nonzero vectors that are orthogonal to v = (-1,5,2)

A: This is a simple problem based on orthogonal vector which could be solved by using basic knowledge…

Q: Find the components of the vector V with point p1 (1,4,5,3). And its ending point p2 (2,5,86) I need…

A: Given point is : p1=1,4,5,3 and p2=2,5,8,6 To find the component of the vector V.

Q: Write the vector (7,8, –8) as a linear combination (if possible) as of the vectors (-1,1,2), (2,3,…

A: See answer below

Q: Select all vectors parallel to the vector (1,-3, 5). O (2, -6, 10) 0(-1,3,6) - 15

A: here to we need to find the parallel vectorsto the given vector from the given options. the solution…

Q: let the vectors u = (- 2, -9, -8) and v = (- 4, -4, T) the value of T so that u and v are…

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Q: Let v1 = [1, 1, 0, 2], v2 = [0, 1, 2, 3], V3 = [-1, 0, 2, 1], V4 = [ 3, 1, -4, O] and b = [4, 3, -2,…

A: According to the given information, it is required to find the solutions to the vector equation.

Q: 2. Write the vector v = (1,3,2) as a linear combination of vectors u = (1,2,1), %3D (2,6,5), uz =…

A: We have to write a vector v to a linear combination of the vectors u1, u2, u3

Q: Determine whether the vectors u = (-3,9,6) and v = parallel, (4, –12, –8) are orthogonal, or…

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Q: Determine the tail of the vector whose head is (3, −2, 2).

A: We have to determine the tail of the vector whose head is 3, -2, 2 and position vector is: 24-1 We…

Q: Determine if the vectors (2, –2, 1) and (0,1, 2) are orthogonal.

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Q: Express i = (3,7,-4) as a linear combination of i = (1,2,3), ỷ = (2,3,7), z = (3,5,6), also check…

A: see below the answers

Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1)

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Express the vector x as a linear combination of the u's. U₁ = 0, U₂ = 5, -1.4 U3 Ox=-3u₁ +4u2 +243…

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Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: If the vector v has initial point P, what is its terminal point? V3 (23, -5, 13), Р(-6, 4, 2) (х, у,…

A: vector= terminal point - initial point P= initial point=(-6,4,2) v=(23,-5,13) terminal point =…

Q: 4. Write the vector (1, 2, –2) as the sum of two vectors: one that is parallel to the vector (1, 1,…

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Q: Write the component form of a vector v with initial point P(8.6, -2.5) and terminal point Q (6.7,…

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Q: Write the vector (7, 8, -8) as a linear combination (if possible) as of the vectors (-1, 1, 2), (2,…

A: Let the linear combination be, x-112+y23-2=78-8 It is required to determine the value of 'x' and 'y'…

Q: Show that the column vectors (1,1,2,4), (2,-1.-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are…

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Q: 24. Write a vector (-3, 22, -3) as a linear combination of the vectors (-1, 2, 3) and (0, 4, -3).

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Q: Write the vector (7, 4,-12) vectors (-2, 1, 2), (1, 1, –2) as a linear combination (if possible) as…

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