3 1 V1 V3 V4 V5 -2 4 6. Without calculations, determine if the set of vectors, S= {v1, V2, V3, V4. V5}, is linearly dependent or independent. S consists of 5 vectors in R*. Determine whether the set of vectors, T = {v1, V2, V3, v4}, is linearly dependent or А. В. %3D independent using the rank of the matrix composed of the vectors in T. Determine whether the set of vectors, Q = {v1, v3, V4, V5}, is linearly dependent or independent using the determinant of the matrix composed of the vectors in Q. D. С. Show that v5 can be written as a linear combination of v1, v2, V3 and v4 by solving for the constants c,, C2, .. and c, in the equation c,V, + c2v2 + .…+ C4V4 = V5- From your results of part a, b, c, and d, what is the span of a. vi and v2 b. Vi, V2, and V3 с. Т, Q апd S Е.

Q: Determine whether or not the vectors u=(1, 1, 2), v=(2, 3, 1), w=(4, 5, 5) in R3 are linearly…

A: Given vectors, u=(1, 1, 2), v=(2, 3, 1), w=(4, 5, 5) in R3

Q: b) Give an example of 5 linearly independent vectors in R*, or explain why it is impossible to do…

A:

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v1, v2, and v3…

A: Consider the vectors v1 = (1, 0, 1), v2 = (−1, 1, 2), v3 = (0, 1, 3) We have to find nontrivial way…

Q: 3) Check whether the vectors V, =[1 3 3 s,V, =[3 10 6 7]°,V, = [2 7 3 2] linearly are independent.

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

A:

Q: 5. Determine whether the set of vectors are linearly de- pendent or independent. Explain results…

A:

Q: 1. Determine whether the vectors īi and 74 = are 0 linearly independent or linearly dependent.…

A:

Q: 4 2 Vị V2 8. V3 4 4 Given a1 2, a2 = 5, and az = 3, what vector is formed by the linear combination…

A:

Q: [C] Is the system of vectors X1 = (2, 2, 1)", dependent? Ху — (1,3, 1)7, X3 = (1, 2, 2)" linearly

A:

Q: () (3) The vectors and are Select one: a. Linearly dependent b. Linearly independent

A:

Q: b) Find values of h for which the vectors are linearly dependent. Justify your answer. 5

A:

Q: Q6) For which values of x are the following vectors linearly independent? 2 3 w = 1 %3D -2 1

A: We have to find the value of x where u,v and w are linearly independent

Q: 5. u = Write the linear combination of standard vectors i and j.

A:

Q: a). Determine if the set of vectors  V= {v1,v2,v3}, is linearly independent v1 =  -1 3 0 v2 =  2…

A: (A) To determine whether the below set of vectors are linearly independent or not. v1=−130, v2=2−33,…

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v1, v2, and v3…

A:

Q: For what value or values of k the vectors V1 = (1,0, –2,0), V2 = (-1,k,–2,0), V3 = (1,1,1,2) are ▼4…

A: A set of vectors are linearly dependent if there exist scalars not all zero such that  . A system…

Q: 2. Consider the following vectors 3 V1 = Vz = -2 V3 -4 2 a) Show that V1, V2 are linearly…

A:

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

A:

Q: (d) Let w =(-39,22), v’i=(2–5), v°2=(5,-4), v°3=(-4,-1). If possible, express w as a linear…

A: In this question we need to multiply vectors by constant and have to find values of constant

Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

A:

Q: Which of the following sets of vectors in R² is linearly dependent? A. {(1,0), (0, 1)} B. {(1,0),…

A: A set of vectors is said to be linearly independent if the matrix with these vectors as columns has…

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

A:

Q: Choose the linearly dependent vectors in R Select one: -2 b. d. 2.

A: From a given set of four vectors we need to find the set of vectors which is linearly dependent in…

Q: Consider the vectors V1, V2, V3 and b. 1 2 8 -2 V1 ,V3 -13 6. 12 18 Write b as a linear combination…

A:

Q: B)Find value of h for which the vectors are linearly independent, justify answer

A: 2-24 , 4-67 ,-22h

Q: (2) Determine if the vectors are linear independent or linear dependent. Justify your answer. (a)…

A:

Q: Are the vectors V₁ = 2 1 1 V₂ = 1₂V3 3 4 1 linearly independent? -9

A:

Q: Determine if the following sets of vectors is linearly independent or linearly dependent. Justify…

A: We want to see given vectors are linearly dependent or independent.

Q: Write the vector 3 (if it is possible) as a linear combination of the vectors d1, d 2.

A:

Q: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

A: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

Q: a) Find the value(s) of c for which the following vectors vị ‚V2 = 1 |and v4 Ea -1 are linearly…

A:

Q: Determine if the vector 2 b = 3 5 can be written as a linear combination of the vectors V₁ = 1 and…

A:

Q: Which of the following vectors are linearly independent? (2) (0) 21

A:

Q: Given that the set of vectors {v1, v2, v3}, where the vectors belong to R3 are linearly independent.…

A:

Q: Choose the linearly dependent vectors in R'. Select one: а. O b. O d. -2

A: The solution is given below

Q: 3) Check whether the vectors V, =[1 3 3 5]. V. =[3 10 6 7].V, = [2 7 3 2 are linearly independent.

A:

Q: 3) Check whether the vectors V, =[1 3 3 5.V =[3 10 6 7]'.v, = [2 7 3 2] e linearly are independent.

A:

Q: a) Let S = {v1, v2, V3} be a linearly independent set of vectors in R³. Determine whether T = {2v1…

A:

Q: C. Is Så 5. Let V = R2 and let S be the set of vectors {[:[}} S = {v1,V2} %3D -3 Is S is linearly…

A:

Q: })- The vectors and are Select one: a. Linearly dependent b. Linearly independent

A:

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v2, and vz…

A: Given vectors are v1 = (1, 0, 1) v2 = (-1, 1, 2) v3 = (0, 7, 4)

Q: Which sets of vectors are linearly independent and which are not? 4 2 6. 9 0. 3. 2. 3. 2. 2. 1.

A:

Q: Q3: Are the following vectors linearly dependent or independent? 1) (3,4), (4,3)

A:

Q: Find the value(s) of h for which the vectors are linearly dependent. [1 [1 3 4 10. 3 11.-5 8. -3 -2…

A:

Q: Q3: Are the following vectors linearly dependent or independent? 2) (1,4,5), (4,4,8), (3,–3,0)

A: We will check if the determinant of the matrix formed by the given vectors is zero or not.

Q: Q3/ Determine whether the given vectors are orthogonal, parallel or neither: (1) u =(-2, 6, -4) , v…

A: Given that two vector u and v and prove that its orthogonal , parallel or neither.     Here i…

Q: Determine if the vector v is a linear combination of the remaining vectors.

A: Given vectors are : v =3.22.0-2.6,  u1 = 1.00.44.8 ,  u2 = 3.41.4-6.4 , u3 = -1.20.2-1.0 If the…

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

A:

Q: 6. Determine if the vectors vi = (1,–1,3, –1), v2 = (1, –1,4, 2), v3 = (1, –1,5, 7) are linearly…

A:

Q: Determine whether the set of vectors in M2.2 is linearly independent or linearly dependent. -2 52 2…

A: A= [2  -2]     B = [5  2]            C = [2  -7]       [5  4]             [-3  3]…

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.