Problem 2: (2 If V = R' is a vector space and let H be a subset of V and is defined as H = {(a,b,c):a² +b² = 0,c<0}. Show that H is not a subspace of vector space. %3D %3D

Q: The set of vectors in R? with y = -3x is a real vector space

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Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x°, -1+a…

A: given B=1+x-2x2 , -1+x+x2 , 1-x+x2B'=1-3x+x2, 1-3x-2x2 , 1-2x+3x2 b) find the coordination matrices…

Q: Suppose U, W,, W, are subspaces of a vector space V. Show that (Un W,) + (UnW,)Cun (W, + W,) Find…

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Q: If V is a vector space then show that cV=V.

A: Vector space: A non-empty set V closed with two binary operations called addition and scalar…

Q: If V is a vector space than show that cV=V

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Q: 6. (a) Let u, v, w be three linearly independent vectors in Euclidean Space R^7. Determine a value…

A: we have to find the value of for the linearly dependent and linearly independent

Q: Question 2 Is (u, v) = au₂v₁ + bu₂V₂ +bu₂V₂ + €₂V₂, where u = (₁, ₂) and v = (₁, ₂) are vectors in…

A: Given : u , v=au1v1+bu1v2+bu2v1+cu2v2 To Prove : Inner product .

Q: 1. Let, p is the set of all vectors of the form: m,n, te R. 2n (a) Is p closed under vector…

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Q: Consider the line V = {(t,t + 1) |t € R} in R. Let V be the real vector space with vector addition e…

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Q: 27. Let S be the set of all vectors both of y in R' such that x + y -z = 0 and 2x – 3y + 2z = 0.…

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Q: - 15 - 13 -1 Let y = and v2 Find the distance from y to the subspace W of R“ spanned by v, and v2,…

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Q: Consider set V = { (x, y ), x,yER} with the following operations: addition (x1, y1) + (x2 , Y2) = (2…

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Q: (i) Consider the vector space M2×2 with the trace inner product ( A,B) = trace(A'B) and let A = .…

A: We are entitled to solve only one question at a time. Given - To find -

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: H.W: Let V = R2, defined the addition by: (u1 +u2) + (V1 +v2)= ( U1 +V1 , U2 +V2 + 1) With standard…

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Q: If V is vector space, with u = (u, , U2) and v = (v, , v2) with u +v = (u,+v, , u2+v2) and ku =…

A: u=(u1,u2) , ku=(3u1,0) k=2, u=(-1,2)

Q: A student learning about linear independence makes the following inaccurate statement: "A subset S…

A: We have to solve given problem:

Q: Let S be the space of all complex vectors (x, y, z) such that y = z². Determine whether or not S is…

A: In the given problem we verify the properties of vector addition

Q: Determine whether W is a subspace of V

A: Determine whether W is a subspace of V

Q: A: Prove that a vector (2,-1, 1) is in the vector space W =span((2, 1, 3), (4, 0, 4)) and that (3,…

A: Vector space, W=span2, 1, 3, 4, 0, 4Vectors : 2, -1, 1 and 3, 2, 7

Q: Question 3. Let (X,r) be a topological space and YCX. Show that if the subspace (Y,r,) is connected,…

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Q: If scalar multiplication and addition is redefined on R² in the following way, show that it is NOT a…

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Q: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

Q: Q4. Consider a vector space that consists of the linear combinations of the following functions: {1,…

A: We will solve this by the help of definition of basis and dimension of vector spaces

Q: For what value(s) of the parameter p is the vector space described by the set of vectors {v1 = (-1,…

A: Approach to solving the question: Detailed explanation: Examples: Key references:…

Q: Explain why the following sets of vectors are not bases for the indicated vector spaces. (Solve this…

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Q: (a) Find the vector Q=[0, a,0] such that the resultant of the vectors: P=[5, 7, 8], Q=[0, a, 0] , R=…

A: Hey, thanx for your question. According to our policy I m answering question first. Please post the…

Q: Consider the three vectors V1 = (1,0,0, –1), v2 = (0, 1, 1, 0), V3 = (1, 1, 1, 1). Let W be the…

A: Given that W be a subspace of R4 spanned by the vectors. v1=(1,0,0,-1), v2=(0,1,1,0), v3=(1,1,1,1)…

Q: Consider the vectors v1, v2, ..., Um in R". Is span (01,..., īm) necessarily a subspace of R" ?…

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Q: True/False: If V is a subspace of R", then dim(V) + dim(V+) = n. True False

A: This is true and follows from a famous theorem in linear algebra.

Q: (3) Let L be the line y 2r in the plane. Find a matrix C such hat for every vector H plane, the…

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Q: Consider the vector space V defined by V = {(x, y, z) | x+y+z=0}. Let u = (1, -2, 1) and v = (3, -1,…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: The inner product, (alb), of any two vectors a and b in a vector space must satisfy the conditions…

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Q: Does the set of all functions that vanish at x = 0 and x = L form a vector space? If it does,…

A: 1) Commutativity of addition: Let f(x) and g(x) be functions in V.Then, .Therefore, addition is…

Q: Any given vector space may have distinct inner products.  True  False.

A: Given :- Any given vector space may have distinct inner products. To find :- The given statement is…

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.