For each of the following operators T on R³ H 00 -2 0 1 (a) 10 1 Solve x' Tx where T is the operator in (a) Introduce the new basis (1, 0, 0), (0, –√2, √2), (1, -2, -1), and new coordinates (y₁, y2, y3) related to the old by The general solution is Therefore In the new coordinates the differential y₁ Y/₂ y3 = √2 y₂. X1 = x2 = x3 = Yı Y2 Y3 x1 = X2 X3 = = Y₁ + Y3, -√2 Y₂2 √2 Y2 equation becomes Y, - -√2 Y31 - 2y3, Y3. Cet, A cos (√2 t) + B sin (√2 t), -B cos (√2 t) + A sin (√2 t). Cet B cos (√2 t) + A sin (√2 t), (2B - A√2 ) cos (√2 t) - (B√2 + 2A) sin(√2 t), (B + A√2 ) cos (√2 t) + (B√2 − A) sin (√2 t).
For each of the following operators T on R³ H 00 -2 0 1 (a) 10 1 Solve x' Tx where T is the operator in (a) Introduce the new basis (1, 0, 0), (0, –√2, √2), (1, -2, -1), and new coordinates (y₁, y2, y3) related to the old by The general solution is Therefore In the new coordinates the differential y₁ Y/₂ y3 = √2 y₂. X1 = x2 = x3 = Yı Y2 Y3 x1 = X2 X3 = = Y₁ + Y3, -√2 Y₂2 √2 Y2 equation becomes Y, - -√2 Y31 - 2y3, Y3. Cet, A cos (√2 t) + B sin (√2 t), -B cos (√2 t) + A sin (√2 t). Cet B cos (√2 t) + A sin (√2 t), (2B - A√2 ) cos (√2 t) - (B√2 + 2A) sin(√2 t), (B + A√2 ) cos (√2 t) + (B√2 − A) sin (√2 t).
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 answer has been given, please prove the process
question about :APPLICATION OF COMPLEX
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 3 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,