The goal of this exercise is to find a least square solutions of a matrix equation Ax = b where D-[1] b= by calculating the projection of the vector b onto the column space of the matrix A. a) Compute an orthogonal basis of the matrix A. then you should do it as follows: A = How to enter a set of vectors. In order to enter a set of vectors (e.g. a spanning set or a basis) enclose entries of each vector in square brackets and separate vectors by commas. For example, if you want to enter the set of vectors 2 0 2 1 Enter an orthogonal basis of the column space of A: {HD} 2 [5,-1/3, -1], [-3/2, 0, 2], [-1, 1/2, -3] b) Use part a) to compute the vector projcol(4)b, i.e. the orthogonal projection of b onto the column space of A. Enter the vector projcal(4)b in the form [c₁, C₂, C3]: c) Solve the matrix equation Ax = projcl(4) b. Its solutions are the least square solutions of the original equation Ax = b. Enter the vector x of least square solutions of Ax = b in the form [x₁, x2]:
The goal of this exercise is to find a least square solutions of a matrix equation Ax = b where D-[1] b= by calculating the projection of the vector b onto the column space of the matrix A. a) Compute an orthogonal basis of the matrix A. then you should do it as follows: A = How to enter a set of vectors. In order to enter a set of vectors (e.g. a spanning set or a basis) enclose entries of each vector in square brackets and separate vectors by commas. For example, if you want to enter the set of vectors 2 0 2 1 Enter an orthogonal basis of the column space of A: {HD} 2 [5,-1/3, -1], [-3/2, 0, 2], [-1, 1/2, -3] b) Use part a) to compute the vector projcol(4)b, i.e. the orthogonal projection of b onto the column space of A. Enter the vector projcal(4)b in the form [c₁, C₂, C3]: c) Solve the matrix equation Ax = projcl(4) b. Its solutions are the least square solutions of the original equation Ax = b. Enter the vector x of least square solutions of Ax = b in the form [x₁, x2]:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The goal of this exercise is to find a least square solutions of a matrix equation Ax = b where
2
-83-8
A = 0 2
b=
1
by calculating the projection of the vector b onto the column space of the matrix A.
a) Compute an orthogonal basis of the matrix A.
How to enter a set of vectors.
In order to enter a set of vectors (e.g. a spanning set or a basis) enclose entries of each vector in square brackets and separate vectors by
commas. For example, if you want to enter the set of vectors
then you should do it as follows:
(0)
2
Enter an orthogonal basis of the column space of A:
-3
[5,-1/3, -1], [-3/2, 0, 2], [-1, 1/2, -3]
b) Use part a) to compute the vector projcol(4)b, i.e. the orthogonal projection of b onto the column space of A.
Enter the vector projcal(4)b in the form [C₁, C₂, C3]:
c) Solve the matrix equation Ax = projc.l(4) b. Its solutions are the least square solutions of the original equation Ax = b.
Enter the vector x of least square solutions of Ax = b in the form [x1, x₂]):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb493ecdd-cbdc-400d-a05a-de2010eb2d52%2Fae667864-ac21-4a09-9767-4b4f1c3f8131%2F1d6y86d_processed.png&w=3840&q=75)
Transcribed Image Text:The goal of this exercise is to find a least square solutions of a matrix equation Ax = b where
2
-83-8
A = 0 2
b=
1
by calculating the projection of the vector b onto the column space of the matrix A.
a) Compute an orthogonal basis of the matrix A.
How to enter a set of vectors.
In order to enter a set of vectors (e.g. a spanning set or a basis) enclose entries of each vector in square brackets and separate vectors by
commas. For example, if you want to enter the set of vectors
then you should do it as follows:
(0)
2
Enter an orthogonal basis of the column space of A:
-3
[5,-1/3, -1], [-3/2, 0, 2], [-1, 1/2, -3]
b) Use part a) to compute the vector projcol(4)b, i.e. the orthogonal projection of b onto the column space of A.
Enter the vector projcal(4)b in the form [C₁, C₂, C3]:
c) Solve the matrix equation Ax = projc.l(4) b. Its solutions are the least square solutions of the original equation Ax = b.
Enter the vector x of least square solutions of Ax = b in the form [x1, x₂]):
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
