Explanation Given: The given matrix is: [ 6 − 3 2 1 ] Procedure used: Finding the eigenvalues and eigenvectors: Expanding the determinant of | A − r I | = 0 and then, solve the n th–degree polynomial in r . Therefore, finding the eigenvalues is equal to the finding the zero of the polynomial. The above expression is called characteristics equation. The corresponding nontrivial solutions r are called eigenvectors and It get by solving the ( A − r I ) u = 0 Here, u = [ u 1 u 2 ] . Calculation: Consider the matrix: A = [ 6 − 3 2 1 ] Substitute the value of matrix A in the characteristic equation and solve for r : | [ 6 − 3 2 1 ] − r [ 1 0 0 1 ] | = 0 | [ 6 − 3 2 1 ] − [ r 0 0 r ] | = 0 | [ 6 − r − 3 2 1 − r ] | = 0 ( 6 − r ) ( 1 − r ) + 6 = 0 Further simplify as: ( 6 − r ) ( 1 − r ) + 6 = 0 6 − 6 r − r + r 2 + 6 = 0 r 2 − 7 r + 12 = 0 r 2 − 4 r − 3 r + 12 = 0 Further simplify as: r ( r − 4 ) − 3 ( r − 4 ) = 0 ( r − 3 ) ( r − 4 ) = 0 Take first factor: ( r − 3 ) = 0 r = 3 Take second factor: ( r − 4 ) = 0 r = 4 Therefore, the eigenvalues are r 1 = 3 and r 2 = 4 Find the eigenvector corresponding to eigenvalue r 1 = 3 by using the formula. ( A − r I ) u = 0 : ( A − r I ) u = ( [ 6 − 3 2 1 ] − 3 [ 1 0 0 1 ] ) [ u 1 u 2 ] = ( [ 6 − 3 2 1 ] − [ 3 0 0 3 ] ) [

7th Edition

ISBN: 9780135902738

Author: Nagle

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 9.5, Problem 2E

To determine

To find:

The eigenvalues and eigenvectors for the given matrix.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.5, Problem 1E

Chapter 9.5, Problem 3E

Students have asked these similar questions

Assuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fP

Find the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.

3) Recall that the power set of a set A is the set of all subsets of A: PA = {S: SC A}. Prove the following proposition. АСВ РАСРВ

Chapter 9 Solutions

MYLAB MATH-W/ETEXT F/FUND.DIFF.EQUAT.

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The eigenvalues and eigenvectors for the given matrix.

Solution Summary: The author explains how to find the eigenvalues and enumerates the nontrivial solutions for the given matrix.

Videos

To find: The eigenvalues and eigenvectors for the given matrix.

Want to see the full answer?

Chapter 9 Solutions

To find:

The eigenvalues and eigenvectors for the given matrix.