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

See similar textbooks

Related questions

Question

Box answer

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

Expert Solution

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

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
Box answe
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
Box answer
Box answer
Let 1 A = -2 1 Consider the system of equations = A. (a) Find all eigenvalues of A. (b) Show that 7 = 0 is the only equilibrium solution of the system. %3D (c) Determine whether 7 Ở is a node, or a saddle, or a spiral point. (d) Determine the stability of 7 = 0. 2.
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?
V2 -V2 -V2/2 V2/2 -1 1 1 A = -1 You should be able to complete each step by hand. (a) Find the eigenvalues of A" A, A1 > A2 > A3 2 0. (b) Find a complete orthonormal set of eigenvectors {v1, v2, V3}, where v; is an eigen- vector for Ai. (c) Set up the 4 × 3 matrix E with Ei = 0; = VA; (the ith singular value) and all other Eiji = 0. (d) Find u; the left singular vectors. Recall u; = Av; for i = 1,2,3 and u4 is a basis for NS(A"). (e) Let U = [ui u2 u3 u4] and V = [v1 v2 v3]. (f) Verify that A = UEVT. This all works out very nicely for this carefully chosen matrix A.

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS