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 = (7, -6, 14) Z = () v-(1, -) 43 v = 13, 4 V = (c) w = (4, -7, 13) w = (d) u = = (5, 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: Find the initial point of the vector that is equivalent to u = (2, 2, 4) and whose terminal point is…

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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: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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Q: {(0, 1,-1), (1,2, ).( 3,-1,4)}

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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: 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: sketch the vectors AB and PÓ, and determine whether they are equivalent. А %3 (1,4), В %3 (-6, 3),…

A: Given points are: A=1,4 ; B=-6,3 ; P=1,4 ; Q=6,3 We have to determine whether the vectors AB→ and…

Q: a. Write the vector (-5, 15, 12) as a linear combination of a the form 4a, + 5ã, + 6ã3, which would…

A: Solving system of linear equations we get the result

Q: Find the components of the vector PP2. P1(4, 5, 5), P2( 7, 10, 7) PP2 =( i

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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: Write the component form of a vector v with initial point P and terminal point Q. P(-1,-10), Q(-1,…

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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: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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Q: и, %3 (1,2,1, — 4,1), и, 3 (1,2, —1,2,1), и, — (2,4,1, —5,0), и, — (1,2,3,—10, 1)

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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: Find 2u, -3v, u + v, and 3u 4v for the given vectors u and v. = (-8, 9), v= (8, -2) u = 2u = -3v = u…

A: Given u = {-8, 9} and v = {8, -2}

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Given 2 vectors å = (-2,0,–1), b = (-1,3,1). Which vector is perpendicula å + b and å – b. - O…

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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: Determine if the vectors vị = (1,2, 3), v2 = (1,-1,–3), v3 = (1, 1, 1) span R³.

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

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: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given: S=(2,-1,3),(5,0,4) and u =(2, 1, -1). Consider s1=2,-1,3,  s2=5,0,4.

Q: Which two vectors are orthogonal if given a =,b = and c =

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

A: Explained below

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Consider c1, c2 are constants such that z=c1s1+c2s2. Substitute the values of z, s1, s2 in the…

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: (a) Let w =(-5,-17,7), v 1=(0,-1,1), v² 2=(0,-2,1), v 3=(1,2,-1). If possible, express w as a linear…

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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: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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Q: Vector (3,-2,1) can be written as a linear combination of which of the following vectors? a. {(2, 0,…

A: OA = i + 2j  OB = 3i + 2j Find diagonal vectors and its magnitude. Question 1  solved.  Solving more…

Q: Show that the vectors V, =(1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = (1, -1, -4, 0 ) and V, =(2, 1,…

A: Sind the determinant of the matrix whose rows are given vectors

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 each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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Q: 1. Are the vectors (-3, 0, 4), (5, -1, 2) and (1, 1, 3) linearly dependent in R3? a. Yes b. No

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Q: Find all vectors u that satisfy the equation (1,1,1)×u= (−5,2,3).

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Q: Write the vector v= (5,-5,4) Linear combination of the basis vectors V1(3,0,-6) V2(-4,1,7) and…

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