check whether the set of vectors v1=(-9,-7,-15) ,v2=(1,-1,3), v3=(3,2,5) and v4=(2,1,4) are linearly independent or dependent. show the working details

Q: Determine whether or not the given two vectors are parallel.u =〈-3, 1, 4〉, v =〈6, -2, 8〉

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Q: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

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Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: Express the vector (-1, 0) as a linear combination of the vectors (-1, - 1) and (-1, 1). (-1,0) =…

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Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

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

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Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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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: If u,v and w are linearly independent vectors other than zero vector, are the vectors u, v ,…

A: No, Not Necessarily.

Q: Use vectors to determine whether the points are collinear. (4, −2, 7), (−2, 0, 3), (7, −3, 9)

A: Formula: the vectors a, b and c are collinear if detabc=0.

Q: Show that the vectors v, = (0, 3, 1, -1); v =(6, 0, 5, 1); v (4, -7, 1, 3) form a linearly dependent…

A: Given vectors v1 = (0, 3, 1, -1); v2 = (6, 0, 5, 1); v3 =(4, -7, 1, 3) . Let c1. v1 + c2. v2 + c3.…

Q: Use vectors to determine whether the points are collinear. (0, −2, −5), (3, 4, 4), (2, 2, 1)

A: A(0, −2, −5), B(3, 4, 4) & C(2, 2, 1) be the given points. Now vector joining the points A and B…

Q: 2. Determine whether the set of the vectors {V1, V2, V3, V4} are linearly dependent or independent.…

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Q: Determine if the sets of vectors in Exercise are linearly independent. If for any of these, the…

A: Given :           The vectors are 111 , 123 , 1-12   To determine the vectors are linearly…

Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: Find the Values of for which vectors linearly dependent the are -3 4 -5 8. 6. - 2 6. -8

A: Given that three vectors are linearly dependent.

Q: (b) Determine whether the vectors, , and are linearly independent or linearly dependent.

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Q: Determine if the sets of vectors in Exercise are linearly independent. If for any of these, the…

A: The set S = {v1, v2, v3, v4} of vectors in R4 is linearly independent if the only solution of c1v1 +…

Q: Show that the vectors u1=(1, 1, 1), u2=(1, 2, 3), u3 =(1, 5, 8) span R3

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Q: Determine if the vectors are linearly independent or not

A: The vectors are linearly independent.

Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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

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Q: Determine whether the vectors are linearly independent.

A: Given vectors,  v1=321, v2=120, v3=-12-1 To determine: Whether the vectors are linearly independent.

Q: Use vectors to determine whether the points are collinear. (0, 0, 0), (1, 3, −2), (2, −6, 4)

A: Given:A0,0,0B1,3,-2C2,-6,4

Q: Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Solution:

Q: Determine if the sets of vectors in Exercise are linearly independent. If for any of these, the…

A: Given: vectors 012, 213, 201   To find: If the given set of vectors are linearly independent or…

Q: Use vectors to determine whether the points are collinear (3, 4, −1), (−1, 6, 9), (5, 3, −6)

A: we have to use the vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,-6) are…

Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: 2. ,V2 V3 %3D 3 32 %3D 1.

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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: Use vectors to determine whether the points (0, -2, -5), (3, 4, 4), and (2, 2, 1) are collinear (the…

A: Given points are 0,-2,-5 ,3,4,4 and 2,2,1 Let points 0,-2,-5 , 3,4,4 and 2,2,1 be denoted by P,Q and…

Q: Show that the vectors v, = (0, 3, 1, -1); v, =(6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

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Q: Check whether the sets of vectors (i) ā = {1, 1, 1}, b = {1, 2, 0} , č = {0, – 1, 2} and (ii) ā =…

A: Hi, thank you for the question. Since you have posted multiple questions, as per our policy we…

Q: In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in…

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Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

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Q: Use vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,4) are collinear.

A: The points (3,4,-1), (-1,6,9) and (5,3,4)

Q: Determine if the given vectors are linearly independent or linearly dependent.

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Q: What must be a if the vectors (1,-a,1,1). (-1,a+2,–2, a –1), (0,2, –1,a² +a-4) are linearly…

A: We have to solve given problem:

Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: Check whether the sets of vectors (i) ā = {1, 1, 1}, b = {1, 2, 0} , ĉ = {0, – 1, 2} and (ii) ā =…

A: (1)

Q: Determine every c Є R, for which the vectors [c,1,c], [5,c,4], [9,1,c] are linearly dependent.

A: We will use the property of vectors to determine the values of c for which the given vectors are…

Q: 1 -1 -4 V1 = V2 = 3. , V3 = -1 -4 -1

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Q: Determine if the vectors of R³; vị = (1, –3,0), v2 = (3,0,4) and vz = (11,–6,12) are linearly…

A: Given vectors are: v=(1,-3,0) v=(3,0,4) v=(11,-6,12) Form a matrix by having rows as given vectors.…

Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. {-x + x2,…

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Q: 7. 3. 0. V1 1 V2 8. 1.

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Q: 2a)Use triple scalar to verify that the following vectors are not coplanar. a=[-2,1,0], 5=[-3,4,5],…

A: Given problem:- 2a)Use triple scalar to verify that the following vectors are not coplanar.…

Q: -1 -4 V1 = V2 V3 = 1 -4 -1

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.