Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: (a) Make a change-of-variable substitution z = Py that transforms the quadratic form to one with no cross-product terms. (b) Write down the new quadratic form. (c) Classify the quadratic form as positive definite, negative definite or indefi- nite. 1.1 Q₁(x) = 4x + 4x3 + 4x3 + 4x² +8x1x2 +8x3x4 - 6x1x4 +6x2x3. 1.2 Q2(x) = 2x + 2x2 - 6x1x2 - 6x1x3 - 6x1x4-6x2x3 - 6x2x42x3x4.

Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: (a) Make a change-of-variable substitution z = Py that transforms the quadratic form to one with no cross-product terms. (b) Write down the new quadratic form. (c) Classify the quadratic form as positive definite, negative definite or indefi- nite. 1.1 Q₁(x) = 4x + 4x3 + 4x3 + 4x² +8x1x2 +8x3x4 - 6x1x4 +6x2x3. 1.2 Q2(x) = 2x + 2x2 - 6x1x2 - 6x1x3 - 6x1x4-6x2x3 - 6x2x42x3x4.

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

Using matlab first find the eigenvalues and eigenvectors of the equation. Then do parts a,b and c using matlab 

 

Please show all commands used to compute

Question 1 Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: (a) Make a change-of-variable substitution x = Py that transforms the quadratic form to one with no cross-product terms. (b) Write down the new quadratic form. (c) Classify the quadratic form as positive definite, negative definite or indefi- nite. 1.1 Q₁(x) = 4x + 4x3 + 4x3 + 4x² +8x1x2 +8x3x4 − 6x1x4 + 6x2x3. 1.2 Q₂(x) = 2x² + 2x² − 6x₁x2 − 6x1x3 - 6x1x4 - 6x2x3 − 6x2x4 - 2x3x4.
Transcribed Image Text:Question 1 Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: (a) Make a change-of-variable substitution x = Py that transforms the quadratic form to one with no cross-product terms. (b) Write down the new quadratic form. (c) Classify the quadratic form as positive definite, negative definite or indefi- nite. 1.1 Q₁(x) = 4x + 4x3 + 4x3 + 4x² +8x1x2 +8x3x4 − 6x1x4 + 6x2x3. 1.2 Q₂(x) = 2x² + 2x² − 6x₁x2 − 6x1x3 - 6x1x4 - 6x2x3 − 6x2x4 - 2x3x4.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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