Check whether the set S of all vectors in R¹ given by 126-85=((a+2b₁a+1,a)/a,b ≤ R} is a subspace of R³ or not. Justify your answers.

Q: * +(x) = 3x6-4 (x-k)² +17, the value of the parameter k for f(x) to be a function pair IS?

A: For f(x) to be a function pair  it needs to be one-to-one, which means that each input value must…

Q: Let V₁, V2, V3 be linearly independent vectors in R". Show that {v₁ + V₂, V₂ + V3, V3 + ₁} is also…

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Q: What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean…

A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: Consider V = R^3 and U consists of those vectors each of whose first component is non-negative.…

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Q: Use Axioms only to prove that the the solution to the equation 2x + y + 3z = 0 is a subspace of R³.

A: The given equation .To prove that the solution to the equation is a subspace of .

Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

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Q: Question 1 Let W be the set of all vectors of the form a) [α] b where -2a +6b-6c = 0 Lc -3 Determine…

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Q: Let V = R2, defined the addition by: (u1 +u2) + (V1 + v2)= (U1 +v1 , Uz +V2 + 1) With standard…

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Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

A:

Q: Let W be the set of all vectors of the form ū = H V = [-5s- 2t] 5s + 3t 5s + t . Find vectors ū and…

A: Let S={u,v} be a linear independent set and generate W . Then W=span{u,v} .

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: 9. Show that is a two-dimensional vector. Ai = -x2 X1

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Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: Prove that a set of non -zero vectors {x1,x2,...,xn) is linearly dependent if some of these vectors…

A: A set of non-zero vectors {x1,x2,...,xn} is linearly dependent if some of these vectors say xi is a…

Q: Consider the vector space 2 with the inner product rgk)=x+1,then %3D

A:

Q: What is the dimension of the vector space P°?

A: The dimension of Pn is n+1

Q: A make linearly dependent set of vectors in R^4 Plase make sure you list three different reason why…

A: There are three different reason why the set of vectors is linearly dependent  If a set contains a…

Q: Suppose that three vectors u, v, and w are linearly independent in some vector space. Are the…

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Q: Find the length of the projection of 3   onto the vector -3…

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Q: r- {{: :] T = " E M22| a = - dis a vector space under standard matrix addition and scalar…

A: I have proved T is a subspace

Q: . Prove that two vectors are linearly dependent if and only if one is a scalar multiple of the…

A:

Q: Q-2 Show that the set of all vectors (a-3b, a+2c +4d, b+3c-d, c-d), where a, b, c, d are real…

A: We know that ℝn is a vector space of n tuples and we represent a vector x∈ℝn in the following form:…

Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

A:

Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: 21 Find a basis for the subspace of R³ consisting of all vectors 2 such that -81 + 9x2 + 4x3 = 0 13…

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Q: Determine the is a non-negative integer

A: The number of non-negative integer solution to the vectors…

Q: 9. Determine whether the vectors v₁ = (1,1,2), v₂ = (1,0,1) and v3 = (2,1,3) span the vector space…

A: We know that the dimension of vector space  is 3.If the given three vectors are linearly…

Q: You deposit $2000 in an account with an annual interest rate of r (in decimal form) compounded…

A: Please refer to the solution in next step.

Q: 2. Describe the subspace of R³ (is it a line or a plane or R³?) spanned by (a) the two vectors (1,…

A: Given data:- v1, v2,v3 are vectors in R3.