The eigenvalues of the system + 1 ]y" + 2xy' – 4y = 0 are O A. None of them B. x = -j and x = i C. A1 = -3 and = 4 D. Å1 = -4 and z = 2 E. x = -1 and x = 1

Q: 3. Let A € Mn,n and let λ be an eigenvalue of A. Suppose A satisfies the equation 2A²+5A-10In Show…

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Q: Find the eigen value andeigen vactor 3 -2 2. 56 -3

A: The given matrix is: A=3-2156210-3

Q: The eigenvalues of the system (+1"+2-4y = 0 are O A. A =-3 and = 4 %3D O B. x = -i and x = i O C. A1…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 5. A 3 x 3 matrix is given by A = 0 20 -i 01 (a) Verify that A is hermitian. (b) Calculate Tr (A)…

A: A 3×3 matrix is given by: A=10i020-i01

Q: Match pairs of eigenvalues to the phase portraits of two dimensional systems. A₁ = 1, A₂=2 -A₁-1, A₂…

A: To match the phase portraits of the given eigen values:

Q: Find the eigen values of A = |K [2 -3. a) 1 = -3,4 b) 1 = ±V7 c) 1 = 2+ V3 d) 1 = 3, -4 3.

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Q: 2 0 1 The product of eigenvalues of 4 3 3 0 2 Select one: O a. -2 O b. 2 O c. -10 O d. 10 S.

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Q: .

A: Consider the given matrix is A, such that,

Q: Using Eigenvalues and Eigen Vectors shve Cthe System: *C) =4メ+ y'4) =-2x *24 A=

A: Use the given matrix.

Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

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Q: y" + 3y – 2x = 0 a' + y' – x = 0 (b) Express the as a first order system, and then find the eigen-…

A: Let the system of differential equation is,                                          x1' =a1x1…

Q: 2. For the following systems with complex eigenvalues, find the general solutions: -5 (a) x² = ( 15³…

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Q: 3 1 -3 (iv) C= 1 0 0 L-2 1 2. 3.

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Q: 5 2 22A: Find Eigen values for A = 2

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Q: c-[and D-191 = C = a) Compute: 3C-5D @ @ (iv) C and D. DC det (C) C-¹ b) Find the eigenvalues and…

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Q: Matrix ー45 -40 1. A= 68 59 has complex eigenvalues d= at ib cnd d2= a- ib where a = and b = O. The…

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Q: Find the eigenvalues and bases for the eigenspaces of A³ for -2 -4 -4 A 2 4 2 -2 -2

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Q: Suppose that i Ar. Draw the phase portrait where the 2 x 2 matrix A has %3D complex eigenvalue A =…

A: A phase portrait of a system of differential equation represents the directional behaviour of that…

Q: O A₁2, V₁ = = O A₁2, V₁ = = O A₁-2, V₁ = = The phase portrait shown above is for a linear system…

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Q: [x =3x+2y y = 6x-y

A: Let X'=AX be a system of linear equations, then If the eigenvalues of A are positive , then critical…

Q: When the eigenvalues of a b *-[88] A = 0 d are ₁ = 0 and ₂ = 2, what are the possible values of a…

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Q: Match pairs of eigenvalues to the phase portraits of two dimensional systems. A₁ = -1, A₂=-2…

A: To match the phase portraits of the given eigen values:1). If both the eigen values are of same sign…

Q: 21 2i with vi = -4 + 5i and = -2i with U2 -4 – 5i Write the general real solution for the linear…

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Q: 4. Find the eigenvalues and eigenvectors of A and A³, A-¹ and A - 21: [ A = 1 4 3 3

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Q: dx which statement about the system at = Ax is true? The characteristic polynomial of A is p(x) = λ²…

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Q: a 14. If the complex number 3i is an eigenvalue of a matrix A = (d) a, b, c, d are real numbers,…

A: Solution:Given that, matrix  and the eigenvalue of the matrix A is 3i.

Q: Find Eigenialues and someapording eigeniecdos of Cx = L 16 3.

A: We can solve this using characteristics equation

Q: show that Hhe i'ntegraL equation g(s) -d scsinssinzt) g() 2t has No eigen values.a

A: The details calculation is given below

Q: 2. For the following systems with complex eigenvalues, find the general solutions: -5 ›× - ( 13³ ) ×…

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Q: Let vn = be the solution to the discrete dynamical system: Yn 6xn – 13yn Yn+1 = 0xn – 7yn Xn+1 -3 If…

A: Using diagonalisation of the coefficients matrix.

Q: Problem 21. Let T(x, y) = (x – y, 3x). Then find all eigenvalues and eigen- vectors of T.

A: The given transformation is:T(x, y)=x-y, 3x

Q: Match pairs of eigenvalues to the phase portraits of two dimensional systems. ₁1,4₂ = 2 4₁=-1, 4-2…

A: To match the phase portraits of the given eigen values:

Q: If a real first-order system defined by 1= Ax leads to complex eigenvalues r1,2 = a ±ßi in A, which…

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Q: Find all solutions of the following system of linear equations: dx dt = = 4x + 8y, Xg dy dt = Hi, I…

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Q: Compute the other eigenvector. And draw each of the eigenvectors and the transformed vectors (with…

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Q: Use the eigenvalue method to solve the following system = ri +F 2 -Tị + Tx2, 2

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Q: Use (a) to solve the system x - ( )x. Х. -8 7

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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.