Let H be the set of all points in the third quadrant in the plane V = R². That is, H = {(x, y) | x < 0, y < 0}. Is H a subspace of the vector space V? 1. Is H nonempty?

Q: Determine whether W is a subspace of the vector space V.W = {(x, y): y = ax, a is an integer}, V =…

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

A: Using the orthogonal projection of vector Y to get the component of y along the vector space W.

Q: W = {(x, y): x = 2y}, V= R2 %3D %3D

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

A: Given W be a subspace spanned by the u's, We have to write y as the sum of a vector in W and a…

Q: Let V=R²³ be a vector space over R and w = {{ x, y, z) € R³ : x = y +z, y, z, XER} show that w is a…

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Q: W = {(x, y): y = ax, a is an integer}, V= R² %3D

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Q: | Determine whether the set A forms a subspace in the vector space V where: (a) A is the…

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Q: Let H be the set of points inside and on the unit circle in the xy-plane. That is, let {{]***a :x² +…

A: According to the given information, H be the set of points inside and on the unit circle in the x-y…

Q: Let C[−π, π] be the vector space of functions that are continuous over the interval [−π, π]. Find…

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Q: Let W1 and W2 be subspaces of a vector space V having dimensions m and n, respectively, where m > n.…

A: Given, dimension of W1=mdimension of W2=n such that m≥n   We know, W1∩W2 is a subspace of W1W1∩W2 is…

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: Let S={(a,b) E R²: 2a +b = 1}, then S is not a subspace of the vector space R2.

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Q: Determine whether W is a subspace of the vector space V.W = { f : f (0) = −1}, V = C[−1, 1]

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Q: Determine whether W is a subspace of the vector space V.W = {(x, y): x − y = 1}, V = R2

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

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

A: It is given that V is a vector space and u,v∈V and W={αu+βv|α,β∈ℝ}. The aim is to prove that W is a…

Q: Determine whether the set W={(s, t, s + t) : s and t are real number} is a subspace of vector space…

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Q: "The set U = {(x, y, z, w) E R* | ¤ – y = z + 2w and r + y – z = w + 1} is a subspace." %3D

A: U=x,y,z,w∈ℝ4|x-y=z+2w and x+y-z=w+1 To find: U is a subspace or not Take x,y,z,w=0,0,0,0 Then,…

Q: Let V be an n-dimensional vector space with inner product ( , ). Let U and W be subspaces of V such…

A: Let V be an finite dimensional inner product space and U and W be subspace of V and U∩W=0¯ We have…

Q: Let V be a finite-dimensional vector space, and let U, W be subspaces of V. Prove that (U + W)° C…

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Q: Determine whether W is a subspace of the vector space V.W = {(x, 2x, 3x): x is a real number}, V =…

A: Given: The theorem of test for a subspace explains that if W is a nonempty subset of vector space…

Q: Determine whether W is a subspace of the vector space V.W = {(x, y, z): x ≥ 0}, V = R3

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Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y? + z²) = 0. Is V a subspace of R?

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

A: Let H be the set of all points in the second quadrant in the plane V=R^2. That is,…

Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y?+ z²) = 0. Is V a subspace of R³?

A: Test for subspace for V to be a subspace  If u and v are elements of v then u +av must be in V where…

Q: Let H be a subspace of a vector space V, and suppose that V has dimension d. Which of the following…

A: a) Given a vector space V, let S=v1, ..., v2 be a basis for V. Consequently dimV=d.  Now given H, a…

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: 12. Let K C R" and let V = { E R" : a1y Vy E K}. Prove that V is a subspace of R".

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y²+ z²) = 0. Is V a subspace of R³?

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Q: Determine whether U = {(1, s, t)ls,t e R} is a subspace of R.

A: FOR ANY SUBSET U TO BE A SUBSPACE OF ANY VECTOR SPACE V IT IS NECESSARY THAT U HAS ZERO VECTOR IN…

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

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Q: Let W be the subspace of R spanned by the vectors -2 and Find the matrix A of the orthogonal…

A: Given that  W be the subspace of ℝ2 spanned by the vectors                           1-21  and…

Q: Let V be a finite dimensional vector space over F and let W₁ and W₂ be two subspaces of V. Then,…

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Q: 16. Let V be the set of vectors (x,y, z) E R³ such that r(y² +z²) = 0. Is V a subspace of R³?

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

A: Let W be subspace spanned by u's. Here , u1 = 1101 , u2 = -131-2 , u3 = -1011 Also , y = 644-1 We…

Q: Let W1 and W2 be subspaces of a vector space V having ilimensions mand n, respectively, where m…

A: Let W1  and W2 be the subspaces of finite dimensional vector space V which satisfy dimW1=m  and…

Q: W = {(x, y, z): x 2 0},

A: Given the vector space

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: Let F be the vector space of infinitely differentiable functions from R to R. Consider the subspace:…

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Q: (. Let H be the set of all points in the fourth quadrant in the plane V = R². That is, H = {(x, y) |…

A: We have to answer the following questions.

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: Let W be the subspace spanned by u, and u,. Write y as the sum of a vector in W and a vector…

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Q: Prove that S = {(x, y, z) E R³: 2x + 3y+z = 0} is a subspace of the vector space R3.

A: Explanation of the answer is as follows

Q: Let W be the subspace spanned by u, and uz. Write y as the sum of a vector in W and a vector…

A: Given, y=-243u1=111u2=-16-5 Let, z=xyz is orthogonal to W Since, u1, u2∈W

Q: Let V=R^3 and let H be the subset of V of all points on the plane -3x+5y-5z=0. Is H a subspace of…

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Q: Let W be the subspace spanned by u, and u,. Write y as the sum of a vector in W and a vector…

A: There are two vectors u1 and u2 is given. write the vector y as the sum of a vector in W and 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.