Q1. a. Find the eigen values of the following matrix and discuss the applications of eigen values in engineering disciplines. [25 4 A=0 6-3 00 8 b. Temperature of a disk brake plate at any point (x, y) varies is represented by the T(x,y)=100/(1+x³+y³ ) where T measure in °C and x, y in meters. Find the rate of change of temperature with respect to x direction and y direction and also the rate at a point (2,1).

Q: (c) x': ·(3 = 2₂). x, x(0) = [1,0]T 9 5 -6 -2

A:

Q: Use the power method to approximate the dominant eigenvalue and eigenvector of A. Use th e given…

A: Given : A=948415-48-49 , x0=111  To find : Eigen value and eigenvector by power method.

Q: x1(t) Let x(t) = be the solution to the discrete dynamical system: x2(t) x1(t + 1) = −8x1(t) +…

A: To solve this discrete dynamical system, we first find the eigenvalues and eigenvectors of the…

Q: Q.3. By using power method find the dominent eigenvalue and eigenvector for the following matrix. A…

A:

Q: Using the attached theorms, Solve dx/dt =2x+4y , dy/dt=-x+6y

A: Reference: Differential Equations, Linear Algebra

Q: Find eigenvalues of characteristic equation 2 3 |-6 3.

A:

Q: 23 Find the eigenvalues of A = 0 9 a. None b. A, = -2, A2= 13 c.A, = 0, A2= 11 d. A, = -2, 12=9 e.…

A:

Q: you have been given the linear syestem. following X'= determine the eigenvectors and the matrix. 3 2…

A:

Q: Consider the linear system A₁ = №₁ ÿ₁(t) = ÿ' a. Find the eigenvalues and eigenvectors for the…

A:

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.

A:

Q: 4. For the 2 x 2 matrix A, indicate which of the following vectors are eigenvectors, and for those…

A: We use the definition of eigenvector to solve the problem

Q: 20 1 Q4: If A.x = Ax, where A =-1 4 -1 determine the eigenvalues of the matrix A and l-1 2 an…

A:

Q: Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow…

A: The phase plane is the graphical representation of all the solution curves of a system of…

Q: Q.2 Use eigenvalues and eigenvectors to solve the (1 1 1) X'=2 1 -1x, i =-1,2,2 0 -1 1

A: Given - X' = 11121-10-11X , λ = -1, 2, 2 To find - Use eigenvalues and eigenvectors to solve the…

Q: 7. For R, let A = Ag = cos sin sin 0 cos sin 0 and B Be= 86). cos cos sin (a) Show that B has an…

A: The rotation matrix in 2D is given.

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

A:

Q: The matrix T has eigenvalues and eigenvectors: with A,-1. with A=- with A- Sive formulas for the…

A: Note: According to our guideline, we will answer the first three subparts of the question as the…

Q: Consider the following system. dx dt Find the eigenvalues and eigenvectors. Number of eigenvectors:…

A:

Q: Let the eigenvalues and eigenvectors of matrix A4x4 be 21 = -5, v1 = d2 = 6, v2 = d34 = -3 + 2i,…

A:

Q: Find the matrix exponential The eigenvalues of A are X₁ = -1 and ₂ = 1. In the event that your…

A:

Q: The characteristic equation is. The eigenvalues are l if A= 1 |-2 |-2 4 a.λ-1,λ = 2,λ 3 O A = - 1,1=…

A: We can calculate eigenvalues By |A-λI|=0

Q: 2.- a) find eigenvalue/eigenvalues and the corresponding eigenvector/eigenvectors of A. b) consider…

A: Given system of differential equationx′=−x+5yy′=−yWhich can be written as in matrix…

Q: It is known that a real matrix A has eigenvalues A₁ = 2 and A₂ = 1 + 2i with corresponding…

A: As per the question we are given two eigenvalues and corresponding eigenvectors of a real matrix A…

Q: Assume v (0) = (1 1 0) T, iterate the matrix until the error value E|<0.005 by using power method.…

A: To compute the dominant eigenvalue and the eigenvector of the matrix, use the equation Ax=λx, where…

Q: 4. Find all eigenvectors of the matrix A = 1 %3D 1 (a) (b) (c) 6. 1 3 (d) (e) 1 1

A: Given :- to find Eigen vectors of the matrix A = 1411 To find Eigen vectors first we need to find…

Q: Q1 Find the eigenvalues and eigen functions for BVP yll + 2yl +(2+1)y = 0, y(0) = 0, y(5) = 0

A:

Q: der the near sy. nd the eigenvalues and eigenvectors for the coefficient matrix. 41 " 6 ÿ' = [-10…

A: The given matrix is, A=64-10-6. To Find: Eigenvalues and eigenvectors.

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: -6 2 |X -3 0 2. Find the eigen value of the system: X' =

A: To find the eigenvalue of the system:

Q: + a. Find the eigenvalues of A matrix and the eigenvectors corresponding to these eigenvalues. 3…

A:

Q: 1. Given matrix A = [² ³1₁ 1/3 apply the power method to approximate (a) the eigenvalue with the…

A:

Q: Q4. Define Dis crete and Invers Discrete Fourier Trans form? Find the Eigenvalues of the given…

A: Solution:

Q: Find all the eigenvalues and eigenvectors of the matrix 1 √2 2 √√2 3 √2 2 √√2 1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use the characteristic equation to find all of the eigenvalues and eigenvectors of the following…

A:

Q: For the system X (4 1) |X, show h- %3D

A: It is given that the system is X'=1α41X. We have to show that how the behaviour of the solution of…

Q: Q2/ Find the mathematical model (differential equations and their Laplace transform) for the…

A:

Q: The eigen value for the system: X'= 4 (A) a =-5,3 (B) 2=5,-3 (C) a= 5,5 (D) None

A:

Q: Find the characteristic polynomial and the eigenvalues of the matrix. 62 26 The characteristic…

A:

Q: (1)-(6210 @ L (3) - (X + Xx+4y) = X. (@) L ( 3 ) = ( 3 ) しい روح

A: (i) The given  linear  transformation is  We know  that   be  the  standard basis  of  Thus, the…