Consider the linear system A₁ = №₁ ÿ₁(t) = ÿ' a. Find the eigenvalues and eigenvectors for the coefficient matrix. [ = = 12 [3] ÿ. and X2 = V₂ b. For each eigenpair in the previous part, form a solution of ÿ' = Aÿ. Use t as the independent variable in your answers. and ÿ₂ (t) c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Yes, it is a fundamental set
Consider the linear system A₁ = №₁ ÿ₁(t) = ÿ' a. Find the eigenvalues and eigenvectors for the coefficient matrix. [ = = 12 [3] ÿ. and X2 = V₂ b. For each eigenpair in the previous part, form a solution of ÿ' = Aÿ. Use t as the independent variable in your answers. and ÿ₂ (t) c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Yes, it is a fundamental set
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the linear system
A₁ =
=
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
ÿ'
=
Zn(t) =
=
-6
12
"
8
ÿ.
and ₂: =
15
b. For each eigenpair in the previous part, form a solution of ÿ' = Aỹ. Use t as the independent variable in your answers.
and ₂(t) =
||
c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions?
Yes, it is a fundamental set
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