Let H be the set of all points in the second and fourth quadrants in the plane V=R^2. That is, H={ (x,y) | xy ≤ 0 }. Is H a subspace of the vector space V? does H contain the zero vector V? is H closed under addition? is H closed under scalar multiplication?

Q: Prove thatII = {(x, y, z)|x – 2y+ 3z = 0}is a subspace of JR³, %3D -

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Q: Let W = {a + bx + cx2 + dx c- 3d = 0} be a subspace of Pg. Then th dimension of W is equal to %3D O…

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A: The fourth option '2' is correct. First find the dimension of W. Write the four vectors that span W…

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Q: Find the projection of the vector v onto the subspace S. S = span

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Q: . Let u₁ = (1, -2, -1), U₂ = (2, 2,-2), and v = = (0, 0, 1). v is not in the subspace W spanned by…

A: In this question, a vector that is orthogonal to a given vector is to be determined. A non-zero…

Q: Let R be the field of real numbers. Then {(x,2y,3z): x, y, z ER}is a subspace of R°(R) ?

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Q: 16 In the vector space R, let u= (1, 2, 3), v -(3, 1, 5), w-(3,-4, 7). Prove that the subspace S…

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

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Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

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Q: Find the projection of the vector v onto the subspace S. 1 1 1 S = span 1 v = projs v =

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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: Find a basis for the subspace given by the plane −3x + 2 y + 5z = 0.

A: Given that, -3x+2y+5z=0

Q: Let W be the subspace of the space of all continuous real- valued functions spanned by {cos2 t,sin2…

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A: Let W be a finite dimensional subspace of an inner product space V. Let T be an orthogonal…

Q: The span of a set of vectors from a vector space V is a subspace of V. true or false?

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Q: Let f be a function in C[-T, 1] with inner product (f,g) = Sf(x)g(x)dx and W be a subspace %3D…

A: Orthonormal basis of W will be vectors vi|vi,vj=0; i≠j1; i=j.

Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

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Q: Find the projection of the vector v onto the subspace S. 1. S = span v = projs v =

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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: Let V be a finite dimensional inner product space and let U and W be subspaces of V . Note: parts…

A: Let V be a real vector space in R3 and for any three vectors u,v,w∈V if we can express these three…

Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: Show that [0, 1] and (0, 1] as subspaces of R with the usual topology are not homeomorphic.

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Q: Explain why the set of vectors V vector subspace of R2 = {[+] -1} ist :x>0, y> -1 is NOT a

A: Given: set of vectors  V=xy:x≥0,y≥-1 Explain why the set of given vectors is not a vector subspace…

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Q: Do vectors of the form {[ ]:x*+y*+z"<1} form a subspace of ie?? please explain what 37

A: The given set is                             xyz : x2+y2+z2≤1 Definition of Subspace: Let V be a…

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Q: Find the projection matrix P that projects vectors in R onto W Let W be the subspace of R spanned by…

A: The inverse of a 2×2 matrix is calculated using the formula: a  b c  d -1=1deta  b c  d d  -b -c  a…

Q: Show that [0,1] and (0,1] as subspaces of R with the usual topology are not homeomorphic.

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Q: 2 Find the orthogonal projection of u = onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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Q: Let V be the vector space of all functions from R to R and W, = (/:(4) = 3 +f(2)} W, =/: 2{3) =(1)}…

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Q: Let V be a finite dimensional inner product space and let U and W be subspaces of V . Note: parts…

A: Let V be a finite dimensional inner product space and let U and W be subspaces of V. (a) If dim U+…

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Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

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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: 4. Consider the vector space RR of functions f: R R. Let U = {f: R → R: f(42)=0}. Show that U is a…

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Q: .Is the set of all vectors of the form b. where a and b are any real numbers, a subspace W of R?…

A: Yes, W is a subspace of R^3.

Q: determine the dimension of the subspace of R3 spanned by the given vectors.

A: Determine the dimension of the subspace of ℝ3 spanned by the given vectors.

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: Find the orthogonal projection of u = 1 onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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Q: Let f be a function in C[-T, 1] with inner product (f,g) = Sf(x)g(x)dx and W be a subspace spanned…

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Q: Let ui = (1, –2, – 1), u2 = (2, 2, -2), and v = (0,0, 1). v is not in the subspace W spanned by u,…

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Q: Let R be the field of real numbers. Then {(x,y,z): x,y,z are rational numbers } is a subspace of…

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Q: Explain why S = {(r,y) : x, y € R, x > 0} is not a subspace of R²

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Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors u;. are orthogonal.)…

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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.