![Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))](https://www.bartleby.com/isbn_cover_images/9780321962218/9780321962218_largeCoverImage.gif)
Set
The solution of the linear system
and set
Solve the perturbed system
![Check Mark](/static/check-mark.png)
Calculate the eigenvector, error and the condition number of A.
Answer to Problem 1E
The solution is
Solution of the perturbed system is
The condition number of A is
Explanation of Solution
Given: The matrix has been given
Concept Used:
Given,
To calculate the eigenvector, we use
Then compute the error from s vector
Calculate the perturb solution using given relation
Compute the error from s vector
Calculate the condition number using function “cond(A)” in MATLAB
Program:
clc clear close all A = round(10 * rand(6)); s = ones(6, 1); b = A * s; x = A \ b; fprintf('Solution to the system:\n'); disp(x); err = x - s; fprintf('Error:\n'); disp(err); t = 1.0e-12; E = rand(6) - 0.5; r = rand(6, 1) - 0.5; M = A + t * E; c = b + t * r; z = M \ c; fprintf('Solution to the perturbed system for t = %.12f:\n', t); disp(z); err = z - s; fprintf('Difference between the solutions:\n'); disp(err); t = 1.0e-04; E = rand(6) - 0.5; r = rand(6, 1) - 0.5; M = A + t * E; c = b + t * r; z = M \ c; fprintf('Solution to the perturbed system for t = %f:\n', t); disp(z); err = z - s; fprintf('Difference between the solutions:\n'); disp(err); t = 1.0e-02; E = rand(6) - 0.5; r = rand(6, 1) - 0.5; M = A + t * E; c = b + t * r; z = M \ c; fprintf('Solution to the perturbed system for t = %f:\n', t); disp(z); err = z - s; fprintf('Difference between the solutions:\n'); disp(err); fprintf('Condition number of A = %f', cond(A));
Quarry:
- First, we have defined the given matrix.
- Then compute the eigenvector.
- Calculate the error.
- Calculate the perturb solution at the given time interval.
- Calculate the condition vector of A.
Want to see more full solutions like this?
Chapter 7 Solutions
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
Additional Math Textbook Solutions
A First Course in Probability (10th Edition)
Elementary & Intermediate Algebra
Pathways To Math Literacy (looseleaf)
Calculus: Early Transcendentals (2nd Edition)
College Algebra (Collegiate Math)
College Algebra (10th Edition)
- A student completed the problem below. Identify whether the student was correct or incorrect. Explain your reasoning. (identification 1 point; explanation 1 point) 4x 3x (x+7)(x+5)(x+7)(x-3) 4x (x-3) (x+7)(x+5) (x03) 3x (x+5) (x+7) (x-3)(x+5) 4x²-12x-3x²-15x (x+7) (x+5) (x-3) 2 × - 27x (x+7)(x+5) (x-3)arrow_forward2 Add the rational expressions below. Can you add them in this original form? Explain why or why not. 3x-7 5x + x² - 7x+12 4x-12 Show all steps. State your least common denominator and explain in words your process on how you determined your least common denominator. Be sure to state your claim, provide your evidence, and provide your reasoning before submitting.arrow_forwardcarol mailed a gift box to her sister the boxed gift weighed a total of 2 pounds the box alone weighed 13 ounces what was the wright of the giftarrow_forward
- Directions: Use the table below to answer the following questions and show all work. Heights of Females 50.0 51.5 53.0 53.5 54.0 1. What is the average female height? 2. What are all the differences from the mean? 3. What is the variance for the female heights? 4. What is the standard deviation of the heights of the females? 5. What does the standard deviation found in number 4 represent? Write your answer in complete sentences.arrow_forward135 metr uzunlikdagi simni 6:3 nisbatda qismlarga am eatingarrow_forwardIn circle T with m, angle, S, T, U, equals, 168, degreesm∠STU=168∘ and S, T, equals, 12ST=12, find the area of sector STU. Round to the nearest hundredth.arrow_forward
- (±³d-12) (−7+ d) = |||- \d+84arrow_forward(z- = (-2) (→ Use the FOIL Method to find (z — · -arrow_forwardMODELING REAL LIFE Your checking account has a constant balance of $500. Let the function $m$ represent the balance of your savings account after $t$ years. The table shows the total balance of the accounts over time. Year, $t$ Total balance 0 1 2 3 4 5 $2500 $2540 $2580.80 $2622.42 $2664.86 $2708.16 a. Write a function $B$ that represents the total balance after $t$ years. Round values to the nearest hundredth, if necessary. $B\left(t\right)=$ Question 2 b. Find $B\left(8\right)$ . About $ a Question 3 Interpret $B\left(8\right)$ . b represents the total balance checking and saving accounts after 8 years the balance would be 16 / 10000 Word Limit16 words written of 10000 allowed Question 4 c. Compare the savings account to the account, You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. A = 11998.70 SINCE 9000 is the principal ( 1+0.036/12)12 times 8 gives me aproxtimately 1997 14 / 10000 Word Limit14 words written of 10000 allowed Skip to…arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9780998625720/9780998625720_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305071742/9781305071742_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305115545/9781305115545_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)