Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider a set of algebraic equations Mx = b where 0.778 -1.222 -0.889 2.111 1 M= 0.889 -0.111 The singular value decomposition of M is M = USV where [-0.540 U=-0.260 -0.774 0.577 0.800 0.613 0.577 0.161 0.577 [2.91 %3= 1.30 0 -0.461 0.348 -0.816 V = 0.034 -0.912 -0.408 0.887 0.216 -0.408 ) Based on this decomposition, show that if an exact solution to Mx = b exists, then it will not be unique. (ii) Determine any value for the vector b such that a solution to Mx = b will exist? %3D (iii) What is the set of all b such that a solution to Mx = b will exist? (iv) For the b of part (ii), determine a solution to Mx = b.

Consider a set of algebraic equations Mx = b where 0.778 -1.222 -0.889 2.111 1 M= 0.889 -0.111 The singular value decomposition of M is M = USV where [-0.540 U=-0.260 -0.774 0.577 0.800 0.613 0.577 0.161 0.577 [2.91 %3= 1.30 0 -0.461 0.348 -0.816 V = 0.034 -0.912 -0.408 0.887 0.216 -0.408 ) Based on this decomposition, show that if an exact solution to Mx = b exists, then it will not be unique. (ii) Determine any value for the vector b such that a solution to Mx = b will exist? %3D (iii) What is the set of all b such that a solution to Mx = b will exist? (iv) For the b of part (ii), determine a solution to Mx = b.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Can you please solve part c&d I include one solution because I can just add two images no more, so sorry for it. I have a solution thank you
3.17. Consider a set of algebraic equations Mx =b where -0.778 -1.222 -0.889 2.111 M= 0.889 -0.111 The singular value decomposition of M is M =USV* where T-0.540 U=-0.260 -0.774 0.577 0.800 0.613 0.577 0.161 0.577 [2.91 %= 1.30 0 -0.461 0.348 -0.816 -0.912 -0.408 -0.408 V = 0.034 0.887 0.216 (1) Based on this decomposition, show that if an exact solution to Mx = b exists, then it will not be unique. (ii) Determine any value for the vector b such that a solution to Mx = b will exist? (iii) What is the set of all b such that a solution to Mx=b will exist? (iv) For the b of part (ii), determine a solution to Mx= b. (v) Using the b of part (ii), determine all solutions to Mx = b. Rather than per- form the calculations, based on the above numbers, please use the notation below to develop a formula for the solution. 07 U= [u, uz uz] S = V = [v, vz vj] 02 where u; and v, are the columns of U and V.
Transcribed Image Text:3.17. Consider a set of algebraic equations Mx =b where -0.778 -1.222 -0.889 2.111 M= 0.889 -0.111 The singular value decomposition of M is M =USV* where T-0.540 U=-0.260 -0.774 0.577 0.800 0.613 0.577 0.161 0.577 [2.91 %= 1.30 0 -0.461 0.348 -0.816 -0.912 -0.408 -0.408 V = 0.034 0.887 0.216 (1) Based on this decomposition, show that if an exact solution to Mx = b exists, then it will not be unique. (ii) Determine any value for the vector b such that a solution to Mx = b will exist? (iii) What is the set of all b such that a solution to Mx=b will exist? (iv) For the b of part (ii), determine a solution to Mx= b. (v) Using the b of part (ii), determine all solutions to Mx = b. Rather than per- form the calculations, based on the above numbers, please use the notation below to develop a formula for the solution. 07 U= [u, uz uz] S = V = [v, vz vj] 02 where u; and v, are the columns of U and V.
ull Verizon ? 9:12 AM 9 92% Step2 b) And Mx = b=>USV"x=b =>U"(USv"x)=U*b =>S(v*x)=U*b (as UTU=I) Let z=V"x and d=U™b. =>Sz=d So, discussing the non-uniqueness property of the solution of Mx=b is the same as discussing for Sz=d. Let b = 62 b3 -0. 540b1 – 0. 260b, + 0. 800b3 0. 613b1 Then d = 0. 774b2 + 161b3 0.577b1 + 0. 577b, + 0. 577b3 ?
Transcribed Image Text:ull Verizon ? 9:12 AM 9 92% Step2 b) And Mx = b=>USV"x=b =>U"(USv"x)=U*b =>S(v*x)=U*b (as UTU=I) Let z=V"x and d=U™b. =>Sz=d So, discussing the non-uniqueness property of the solution of Mx=b is the same as discussing for Sz=d. Let b = 62 b3 -0. 540b1 – 0. 260b, + 0. 800b3 0. 613b1 Then d = 0. 774b2 + 161b3 0.577b1 + 0. 577b, + 0. 577b3 ?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Inequality
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS