Q-4: a) Let S = {v1, v2, V3} be a linearly independent set of vectors in R³. Determine whether T = {2v1 + v2 – 2v3, 4v1 + 3v2 , 3v+ 2v2 – v3} is linearly independent. %3D b) Describe all vectors b| that can be written as linear combinations of the 4 [4] vectors v¡ = V2 = ,V3 = |2

Q: 9

A: We need to determine all the values of the constant a for which the vectors

Q: Two vectors in R- are linearly dependent if and only if they lie on a line through (0,0). Select…

A: It is false.

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

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

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Q: 9. Find all real values of c such that the vectors and are linearly independent.

A: Given matrices are 2c0 and cc+30   We know the formula or the quadratic equation ax2+bx+c=0 is…

Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

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Q: 7 Prove or give a counterexample: If v1, V2, . . . , Vm is a linearly indepen- dent list of vectors…

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Q: 12 2 Determine if the pair of vectors v₁ = 3 V₂ = =-3 are orthogonal. -5 3

A: We have to find whether the given two vectors are orthogonal or not?

Q: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

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

A: Given vectors are: v=123; u1=110; u2=011 If the vector v is a linear combination of the remaining…

Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

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Q: 9. (a) Show that the three vectors v = (0, 3, 1, – 1), V2 = (6, 0, 5, 1), and v3 = (4, –7, 1, 3)…

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Q: -2 [5a] Find the value of a such that the vectors u =a +4 and v = |2 are orthogonal.

A: Please refer the attached image for complete solution. Given: u = -2a+4   1  & v = 5a 2 0 are…

Q: 10. Suppose v1, ..., Vķ are nonzero vectors with the property that v; · v; = 0 whenever i + j. Prove…

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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: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

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Q: (iii) Suppose the vectors u, v, w are linearly independent. Show that the vectors u+ v, u-v, u-2v +w…

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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: Consider the vectors in R2 3 2 (3) Express as a linear combination of the vectors Select one:…

A: Here we have to find the linear combination.

Q: (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

A: (a) The given vectors are: v1=(1,2,3,4), v2=(0,1,0,-1), v3=(1,3,3,3)

Q: a) Determine k so that the vectors (1,–1, k – 1),(2, k, –4) and (0,2 + k, -8) in R³ are linearly…

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

Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

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Q: 5. Suppose vectors ū and i are linearly independent. Show that the vectors w = 2u+3ū and 7= ū+ū are…

A: if u and v are linearly independent then for au+bv=0 implies a=0 and b=0

Q: Find the value of c for which the vectors -2 and c-3 in R'are linearly dependent. Select one: 1 2 O…

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Q: Let v1, v2, vz be the vectors in R defined by 30 -17 7 -3 v2 15 V3 = -14 -12 -14 18

A: Solution is given below:

Q: Q2. (d) Show that u=(-2,3,1,4) v=(1,2,0,-1) and are orthogonal vectors in R4.

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Q: #1: a) Express v = (2,13,6) in R³ as a linear combination of the following vectors vị = (1, 5, – 1),…

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

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Q: 7)  Give an example of 3 nonzero vectors v1,v2,v3 ∈ R3 such that v3 is not a linear combination of…

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

Q: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

A: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

Q: 3 The vectors u = -4 and v = -12 are linearly independent. 6.

A: Given vectors : u=3-42 and v=9-126 . Therefore,  we will test these two vectors to find whether 'a'…

Q: 9. Find all real values of c such that the vectors and +3 are linearly independent.

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

A: a  Let S=v1,v2,v3 be a linearly independent set       of vectors in R3       Given that the set…

Q: 2.10 If A, B, and C are noncoplanar vectors (that is, A, B, and C are linearly independent),…

A: It is given that,  A, B and C are linearly independent vectors. We have to determine that whether…

Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: 2 3. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -3 and v = .3 4

A: What is the inner product of the vector space of 2 by 2 matrices. We assume it is Frobbenius inner…

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

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Q: and v2 = -3 3. be two -8- Question ( Let vi %3D vectors in R. Show that v belongs to span {v1, v2 }.

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Q: a) Detemine whether this set of vectors is orthogonal? Q. No. 3 -2 8. 4 1 b) Detemine if the…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: (a) Show that the vectors v = (0, 3, 1, – 1), vą = (6, 0, 5, 1), and v3 = (4, – 7, 1, 3) fom a…

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Q: 3. Give an example of vectors in R3 that are linearly independent. (show works)

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Q: There are 6 linearly independent vectors in R°. O True False

A: We know that the dimension of the vector space R5 is 5.

Q: Q.5. Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V,…

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Q: Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0),…

A: The solution of the problem is given in the next steps.

Q: Consider the vectors in R 2 1 1 1 V1 13 V2 V3 4 VA 1 1 3 Express (if possible) v, as a linear…

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

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Q: Can vector w = 3 be written as a linear combination of v₁ = 4 4 vector w belong to span{v₁,v₂}? V₂…

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Q: 4. For which value of k the vector u = -2 is a linear combination of the vectors 3 3 V1 = 0 and vz =…

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.