Explanation Given: A = [ 2 0 3 0 1 2 0 0 3 0 0 0 ] and b = [ 5 4 3 5 ] . Approach: Let A be an ( m × n ) matrix, and suppose that the column vectors of A are linearly independent. Let S be an orthogonal matrix such that S A is upper trapezoidal. Given a vector b in R m , let S A and S b be denoted as, S A = [ R O ] and S b = [ c d ] . Then, 1. R is non singular. 2. There is a unique least-squares solution of A x = b , x * . 3. The vector x * satisfies R x * = c . Calculation: The matrix A is in the form [ R O ] , R = [ 2 0 3 0 1 2 0 0 3 ] is a ( 3 × 3 ) upper triangular matrix, and det ( R ) ≠ 0 So, solve R x = c Here, c = [ 5 4 3 ] and x = [ x 1 x 2 x 3 ] For the least-squares solution x * such that ‖ A x * − b ‖ ≤ ‖ A x − b ‖ for all x

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

5th Edition

ISBN: 9780134689531

Author: Lee Johnson, Dean Riess, Jimmy Arnold

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 7.6, Problem 4E

To determine

To find:

A vector x* such that ‖Ax*−b‖≤‖Ax−b‖ for all x.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.6, Problem 3E

Chapter 7.6, Problem 5E

Students have asked these similar questions

(±³d-12) (−7+ d) = |||- \d+84

(z- = (-2) (→ Use the FOIL Method to find (z — · -

MODELING 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…

Chapter 7 Solutions

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 7.1 - In Exercises 16, find a symmetric matrix A such...Ch. 7.1 - Prob. 2E Ch. 7.1 - In Exercises 16, find a symmetric matrix A such...Ch. 7.1 - Prob. 4E Ch. 7.1 - In Exercises 16, find a symmetric matrix A such...Ch. 7.1 - Prob. 6E Ch. 7.1 - In Exercises 712, find a substitution x=Qy that...Ch. 7.1 - In Exercises 712, find a substitution x=Qy that...Ch. 7.1 - In Exercises 712, find a substitution x=Qy that...Ch. 7.1 - In Exercises 712, find a substitution x=Qy that...

Knowledge Booster

$Algebra$

Learn more about

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

A vector x * such that ‖ A x * − b ‖ ≤ ‖ A x − b ‖ for all x .

Solution Summary: The author explains that x*=left[cc2& 3 0& 1& 2, and S be orthogonal matrix.

Videos

To find:

A vector x* such that ‖Ax*−b‖≤‖Ax−b‖ for all x.

Want to see the full answer?

Chapter 7 Solutions

A vector x * such that ‖ A x * − b ‖ ≤ ‖ A x − b ‖ for all x .

Solution Summary: The author explains that x*=left[cc2& 3 0& 1& 2, and S be orthogonal matrix.

Videos

To find: A vector x* such that ‖Ax*−b‖≤‖Ax−b‖ for all x.

Want to see the full answer?

Chapter 7 Solutions

To find:

A vector x* such that ‖Ax*−b‖≤‖Ax−b‖ for all x.