[17 -20-9-22. Consider the matrix A = 82a. w =You can check that it has only one independent eigenvectoreigenvector w so that: (A - λI) W=Hb. w-14]-8, for which λ = 3 is a triple eigenvalue:1=မြဲfor this repeated eigenvalue. Find a generalizedwhere λ = 3 and is the corresponding eigenvector.=C.W =-13d. W =

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Answered: [17 2. Consider the matrix A = 8 2 -20…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Find the eigenvalues and normalized eigenvectors of the following matrix. Note: This one looks like it will lead to a cubic, but multiply it out to get an equation that can be simply solved. 7 1 2 1 7 2 2 2 1
Determine if v is an eigenvector of the matrix A. 6 -1 Select an Answer Select an Answer Select an Answer ✓ 1. A 2. A = 3. A = - 5 2 1 1 -5 -6 3 0 0 -2 -1 -6 1 1 1 0 1 1 1 % 0 0 -8 - 0 0 3 -3 -5 7 -3 5 10 2 10 9 -2 13 0 -5 -5 0 0 9 。 9 V = = V = -2 2
2. (1) Compute all eigenvalues and eigenvectors of the Cartan matrix 2 -1 C = -1 2 -1 -1 2 (2) Diagonalize C (i.e. find Q such that Q-'CQ is diagonal). (3) Is C positive definite?
[3 3 Consider the matrix A = 2 8 A. Calculate both eigenvalues of the matrix. B. Choose only one of the two eigenvalues (does not matter which one), and determine a corresponding eigenvector.
After 25 years, your savings account has now grown to $16,200 and has an interest of 6.1% that compounds continuously. How much did you deposit at the beginning of the account
[5 -6 31 4. For matrix 6 -7 3 one of the eigenvalues equals 2. Find corresponding eigenvector. L6 -6 2]
7. Let A = -2 -2 2 2 -1 4 -2 4 (a). Find the eigenvalues and corresponding eigenvectors for A. (b). Find a matrix P that orthogonally diagonalizes A.
2 2. Find the eigenvalues and eigenvectors of the matrix A= -3 3 3 -4 3 3 2 If A is diagonalizable, find a matrix P and a diagonal matrix D such that P¹AP = D. If A is diagonalizable, calculate A 0 H 2 -3.
Airodyne Wind, Inc., has wind tunnels that can operate vertically or horizontally for evaluating the effects of air flow on a component's PCB response and reliability. The company expects to build a new tunnel that will be outfitted with multiple sensor ports. For the estimates below, calculate the equivalent annual cost of the project. First Cost Replacement Cost, Year 2 AOC per Year Salvage Value Life, Years Interest Rate The equivalent annual cost of the project is $ $-250,000 $-330,000 $-940,000 $280,000 5 11%
2. Find the eigenvalues and eigenvectors for the following matrices 4 3 a. A= 5 6 1 2 -1 0 2 -2 b. А — 0 0 3
Let M be a 2 x 2 matrix with eigenvalues A₁ = 0.3, A2 = -0.25 with corresponding eigenvectors = [2²] ²2² = [9] · V2 Consider the difference equation with initial condition xo That is, write xo = C1V1 + C₂V2 H Write the initial condition as a linear combination of the eigenvectors of M. In general, X = Specifically, X4 V1 = For large k, xk Xk+1 = V₁+ )k v₁+ Mxk A V2 7)k V₂
9. Determine which of the following vectors 1 -1 is an eigenvector of the matrix 1 1 1 1 -1 1 -1 W = -1 -1 1 -1 -1 1 and find the corresponding eigenvalue.

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