Answered: Question 1 (Eigenvalue method) Question… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

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Question 1 (Eigenvalue method)
Question 1. Find the general solution of the homogeneous linear system
below using the eigenvalue method.
1
7-(33) 7
1

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For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.
CAPSTONE Explain how to determine whether an nn matrix A is diagonalizable using a similar matrices, b eigenvectors, and c distinct eigenvalues.
Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret your answer geometrically.
Question 2 (Eigenvalue method) Question 2. Find the general solution of the homogeneous linear system below using the eigenvalue method. - (2) y
Using the Rayleigh quotient form to find the dominant eigenvalue (A () in 3 steps. 2 2 -1 -5 9 -3 (= ;")
Use a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion - Row reduction - Integration
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SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer(s) Label them ( C& D)
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Pls help ASAP. Pls show all work and calculations and pls dont miss any steps.
pls explain to step by step and dont skip any steps. thanks
How do we calculate eigenvectors for repeated eigenvalues and how is it different from how we calculate eigenvectors when we have two roots produced from the characteristic polynomial? For example, in the picture, we have a coefficient matrix for a system of linear differential equations. We calculate that the repeated eigenvalue is 2, and we would solve the equation (A minus lambda) times Z is equal to zero as shown in the other picture. This should give us the vector [1, 1] for our first eigenvector. But how would we use this to solve for the second eigenvector to get two linearly independent solutions?

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