Let X= (1, 2] u (3,4,5,.} and A={2,4,5} and metric defined on X as d(x,y) = |x -yl (1) Find interior of A (2) Find limit points of A ( 3) Find open ball B(3,2) (4) explain if A is closed or not (5) explain if (A,d) is a complete subspace of (X,d)

Q: 1. The linear span of a set S is the (a) largest subspace contained in S. (c) smallest subspace…

A: # As per the guidelines we are entitled to solve one question at a time please resubmit the other…

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d)  are subspaces .

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Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: 4) Which of the following is a subspace of R^3? Justify your answer. i) W={(x,y,z)|x+y+z=0} ii)…

A: We will use two step test for vector subspace to check which one of the given is a subspace R^3. Two…

Q: Let X= (1, 2] u {3,4,5,.} and A={2,4,5} and metric defined on |X as d(x,y) = |x - y %3D Find…

A: In the given question given that set S=(1,2]∪{3,4,5,6........} and A ={2,4,5}and a metric defined on…

Q: 3. Let V1 and V2 be subspaces of R" (over R) Their intersection V=V,nV, is the set of 2 all vectors…

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Q: Let X=(6, 9] u{10,11,.} and A=(9,11,12} and metric defined on X as d(x,y) = |x- yl (1) Find interior…

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Q: Problem 3 Prove that H = {(s, t, 0) | s and t are real numbers} is a subspace of R^3.

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Q: The intersection of an arbitary collection of subspaces of a vector space is also a subspace.

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Q: Determine whether the given set S is a subspace of the vector space V. DA. V = C5 (I), and S is the…

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Q: Let U C R’ be the subspace generated by (1, 1, 1, 0, 1), (2, 1, 0, 0, 1), and (0, 0, 1, 0,0). Let V…

A: The given problem is related with linear algebra. Given that U ⊂ ℝ5 is a subspace generated by 1, 1,…

Q: Let X=(6, 9] u{10,11,.} and A=(9,11,12} and metric defined on X as d(x.y) = |x- yl (1) Find interior…

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Q: 3. Let S, and S, be two subspaces of R such that s, n s, = ((0,0,0,0,.0)) and dimension(S,) =…

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Q: Lemma 7 if Y and W are subspaces, then YC W if and only if W CYw. just prove the lemma by using…

A: To prove that:If and are subspaces, then if and only if .Concept:In linear algebra, when we say…

Q: The set {(x, , x,)' 1 x,+ x, =0} form a subspace of R Select one: O True False

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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: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

Q: show what W = {(a,0,b)| a,b E R)  is a subspace of R^3

A: Given : W={(a,0,b)|a,b∈R}   To Show : W is subspace of R3

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Q: Let V be a vector space and W₁, W2 be subspaces of V. Then verify that W₁ + W₂ = {w₁ + W₂ : W₁ € W₁…

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Q: Let X=(6, 9] u {10,11,...} and A=(9,11,12} and metric defined on X as d(xy) Ix-yl (1) Find interior…

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Q: Let V be the subspace of R' spanned by vi = (1, 3, -2, 2, 3 ), v (1, 4, -3, 4, 2 ), v3 (1, 3, 0, 2,…

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Q: Let W be the subspace of R spanned by v = (1,2,1,1), v2 = (2,2,2,1) and V3= (1,0,1,0). Then the…

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Q: a) Is the set W = {(x, y, 1) | x, y are real numbers} a subspace of R^3 ? (b) Is the set W = {(x,…

A: Subspace test:  Let V be a vector space and W is a subset. The subset W is said to be subspace if it…

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Q: (1 point) Let V = P7, the vector space of all polynomials of degree 7 or less. (a) dim V = (b) If U…

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Q: 7. Let V be a 70-dimensional vector space and let W₁ and W2 be 30-dimensional subspaces. What is the…

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Q: Let X= {3,4,5,....} and A={4,6} and metric defined on X as d(x,y) |= |x - y Find interior of A (1)…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.