et X = {(x,y, z): Vx² + y² + z² <1} be a subspace R° with the standard topology and 0 = (0,0,0). Show that the fundamental gro

Q: T X = R with standard topology { IneN} CR k= Show that the subspace topology on k is discrete.

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Q: Is W a subspace of the vector space V? Justify your answer. 1. Wis subset of V = R3 where a W = {…

A: I just used a test of subspace to check the W is subspace

Q: Let W - (a + bx + cx + dx'l a +b-0 and c - 3d = 0) be a subspace of Py. Then the dimension of W is…

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Q: Let H be the set of points in the second quadrant in the plane V=R^2. That is, H = { (x,y) | x ≤ 0,…

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Q: 3) Suppose TE L(V) and U1, . , Um are subspaces of V invariant under T. Prove that U, ...+ Um is…

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Q: Let H = Span{₁,..., If u € R¹ satisfies vú = v½ u then u belongs to H¹. p} be a subspace of R" . =…

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Q: HConsider the vector space R° (over R) and ZcR consisting of vectors z=(z1, z2 z3), with these…

A: Given Z⊂R3, where R3 vector space.z→=(z1,z2,z3)(a) z1=0(b) z1+z2=0(c) z1+z2=1We have to check in…

Q: If V is the vector space of real valued continuous functions , then show that the set W of all d’y…

A: Our Aim is to show that the set W of all solutions of the differential equation3d2ydx2-5dydx+7y=0…

Q: Let V = {(x, y, 2x – 3y)|x, yɛR}. Prove that V is closed for addition and scalar multiplication i.e.…

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Q: Let W = (a + bx + cx² + dx*lc- 3d = 0}be a subspace of Py. Then the dimension of W is equal to None…

A: To find - Let W = a + bx + cx2 + dx3| c - 3d = 0 be a subspace of P3. Then the dimension of W is…

Q: Let V be a vector space and let u, v € V. If W = {au + Bula, 3 € R}, prove that W is a subspace of…

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Q: Let V be a vector space and let u, v E V. If W = {au + Bula, ß E R}, prove that W is a subspace of…

A: Any subset W of a vector space V is subspace of V if W is itself a vector space under same binary…

Q: Let H be the set of all points in the second and fourth quadrants in the plane V=R^2. That is, H={…

A: ANSWER :

Q: Let V be the set of vectors (x, y, z) E R° such that r(y² + z2) = 0. Is V a subspace of R³?

A: 16. Let V be the set of vectors x, y, z∈ℝ3 such that  xy2+z2=0 We have to check whether V is a…

Q: a. . Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

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Q: 10. Let Y = {(x,y,z)| z=-x}. (a) Is Y a subspace of R³? Justify. (b) Is Y a vector space? Justify.

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Q: Find the orthogonal projection ŷ of y = onto the subspace W = Span { uị u2 5 Ex: 1.23 : ŷ =

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Q: :) Let T : U = р — 2q — 0, р, 9, r, s E R Is U a subspace of M2.2(R), if so, find its basis and…

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Q: For a certain subspace W, the orthogonal projection of the vector y = 3 onto W is ŷ 2. Use this…

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Q: In the vector space of functions f: R → R, find a basis for the subspace spanned by {sin t, sin 2t ,…

A: Solving question by theorem vector space

Q: If Sz is a subspace of R" of dimension 3, then there cannot exist a subspace S, of R* such that Si c…

A: This staement is true.

Q: .a. Is the set of vectors W = {(x,y,z) x,y,z € R,x=z+2} subspace of R³?

A: Given that a) W=x,y,z|x,y,z∈ℝ,x=z+2 of ℝ3. b) W=pt-tq of M22 Check the space W is the subspace of…

Q: Let W = (a + bx+ cx + dx'|a+ b= 0 and c -3d = 0 ) be a subspace of P Then the dimension of W is…

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Q: (b) Let X C[0, 1], be the the space of continuous functions on the interval [0, 1]. %3D Consider X…

A: The given problem is related to a normed space of continuous functions on an interval. Given:…

Q: Is T = {(x,y,z)| x+2 y+3z=0} a subspace of R?

A: Subspace

Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}

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Q: et W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

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Q: Verify Gauss's (Divergence) theorem for the given three dimensional region D and vector field F.…

A: To verify Gauss's theorem for the vector field following three dimensional region D and vector field…

Q: Give a counter example to show that W is not subspace of R³. W=set of (x, y, z) where x + y = 1

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Q: Let W = (a + bx + cx? + dx'la + 2c 0 and b -d 0} be a subspace of P, %3D Then dimension of W is…

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Q: 3) Explain why S, = {(x, y) E R²:y > 0} and S1 = {(x, x²): x E R} are not subspaces of R?. %3D

A: We will solve both these parts using only basic knowledge of subspaces and vector spaces (in clear…

Q: Let U, W be subspaces of R" and assume UnW = {0„}. Prove that dim(U + W) = dim(U)+ dim(W). Here U +…

A: We have to prove given result:

Q: Give a counter example to show that W is not subspace of R³. W=set of (x, y, z) where x + y = 1 6. ,

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R?. %3D

A: Consider the given set. U=x,-x|xinR Let, consider that, f,g∈V And f, and g is defined as.…

Q: 3) Let W = { (x, y, z, t) : x = 0, y = -z } be subset of IR*. Is W a subspace of IR* ?

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Q: 12. Let K C R" and let V = {x € R" : x ly Vy E K}. Prove that V is a subspace of R".

A: " As per the company guidelines we are supposed to solve first question only. Kindly post the other…

Q: Consider the set S = y ER : 3x – 5y = 0, x + z =- . Is this a subspace of R ? Explain why or why…

A: Given set is S=xyz∈R3:3x−5y=0, x+z=4. We have to check whether the set S is the subspace of R3 or…

Q: Suppose that V is a vector space with basis B= {bi | i E I} and S is a subspace of V. Let {B1,... ,…

A: Given that V is a vector space with basis B=bi|i∈I and S is a subspace of V. Let B1,B2,B3,…,Bk be a…

Q: Consider X = {1, 2, 3, 4, 5} where the topology is {U C X|1 E U}. Find a subspace of X which is…

A: Consider the set X = {1,2,3,4,5} where the topology is {U ≤ X : 1 ∈U}. We have to find a subspace of…

Q: Verify that U1 = {(x, y) E R² : y = -2x} is a real vector subspace of R?. hat U2 = {(x,y, z) E R³ :…

A: This a question of linear algebra and vector space.

Q: Consider the set S = yl E R : 4x +6z=7y, x – 13y=0 . Is this a subspace of R ? Explain why or why…

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Q: PUl = 1rn – PU .

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Q: Denote by C[0, 1] , the space of all continuous functions defined on the unit interval [0, 1]. Show…

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Q: Is Y = (x,y,z) | y=z} a subspace of R?

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Q: ) The degree of pa is equal to the dimension of the cyclic subspace Z (a ; T) .

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Q: W e R"|2, > 0 over the field of reals is a subspace of the specified vector space ER"

A: Given that W=x1x2x3⋮xm∈Rm|x1≥0 and V=x1x2x3⋮xm∈Rm The objective is to show that W is subspace of V.…

Q: If B is basis for (x, t) then By = {BnY/BE basis for the subspace topology Ty on y IS 9

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Q: Is Q = {(x,y,z) | x=2y & z=1} a subspace of R?

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Q: Let Uz?la :a,bE R and :c;d eR be two Subspaces of M, CR). Show that U eW= M, IR).

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Q: a) Let X = {fe C[0,1]:f (0) = 0} Y = {g ex :[g (t) dt = 0} %3D Prove that Y is a proper subspace of…

A: Note: According to Bartleby guidelines; for more than one question asked; only the first one is to…

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.