Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Verify that X(t) is a fundamental matrix for the given system and compute X1(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t) = x(t)X(0)x is the solution to the initial value problem x' = Ax, x(0) = x0 - 24e-1 -9e-21 060 -5 x'= 10 1x, x(0)= 8e3t x(t)= 1 1 0 -4e-t 3e-21 3t 4e -2 -20e-t 3e-21 3t 4e 060 (a) If x(t) = [×₁ (t) x2(t) ×3(t)] and A = 10 1 validate the following identities and write the column vector that equals each side of the equation. 1 1 0 ×₁' = Ax₁ = x2' = Ax₂ = x3' = Ax3 (b) Next, compute the Wronskian of X(t). W[x()()()]= Since the Wronskian is never and each column of X(t) is a solution to x' = Ax, x(t) is a fundamental matrix. (c) Find x(t) = ☐ (d) x(t) = x(t)x¯1 (0)x₁ =

Verify that X(t) is a fundamental matrix for the given system and compute X1(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t) = x(t)X(0)x is the solution to the initial value problem x' = Ax, x(0) = x0 - 24e-1 -9e-21 060 -5 x'= 10 1x, x(0)= 8e3t x(t)= 1 1 0 -4e-t 3e-21 3t 4e -2 -20e-t 3e-21 3t 4e 060 (a) If x(t) = [×₁ (t) x2(t) ×3(t)] and A = 10 1 validate the following identities and write the column vector that equals each side of the equation. 1 1 0 ×₁' = Ax₁ = x2' = Ax₂ = x3' = Ax3 (b) Next, compute the Wronskian of X(t). W[x()()()]= Since the Wronskian is never and each column of X(t) is a solution to x' = Ax, x(t) is a fundamental matrix. (c) Find x(t) = ☐ (d) x(t) = x(t)x¯1 (0)x₁ =

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
Verify that X(t) is a fundamental matrix for the given system and compute X1(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t) = x(t)X(0)x is the solution to the initial value problem x' = Ax, x(0) = x0 - 24e-1 -9e-21 060 -5 x'= 10 1x, x(0)= 8e3t x(t)= 1 1 0 -4e-t 3e-21 3t 4e -2 -20e-t 3e-21 3t 4e 060 (a) If x(t) = [×₁ (t) x2(t) ×3(t)] and A = 10 1 validate the following identities and write the column vector that equals each side of the equation. 1 1 0 ×₁' = Ax₁ = x2' = Ax₂ = x3' = Ax3 (b) Next, compute the Wronskian of X(t). W[x()()()]= Since the Wronskian is never and each column of X(t) is a solution to x' = Ax, x(t) is a fundamental matrix. (c) Find x(t) = ☐ (d) x(t) = x(t)x¯1 (0)x₁ =
Transcribed Image Text:Verify that X(t) is a fundamental matrix for the given system and compute X1(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t) = x(t)X(0)x is the solution to the initial value problem x' = Ax, x(0) = x0 - 24e-1 -9e-21 060 -5 x'= 10 1x, x(0)= 8e3t x(t)= 1 1 0 -4e-t 3e-21 3t 4e -2 -20e-t 3e-21 3t 4e 060 (a) If x(t) = [×₁ (t) x2(t) ×3(t)] and A = 10 1 validate the following identities and write the column vector that equals each side of the equation. 1 1 0 ×₁' = Ax₁ = x2' = Ax₂ = x3' = Ax3 (b) Next, compute the Wronskian of X(t). W[x()()()]= Since the Wronskian is never and each column of X(t) is a solution to x' = Ax, x(t) is a fundamental matrix. (c) Find x(t) = ☐ (d) x(t) = x(t)x¯1 (0)x₁ =
Expert Solution
steps

Step by step

Solved in 2 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
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