onsider the linear system A₁ = 0 v1 = ÿ₁(t) = a. Find the eigenvalues and eigenvectors for the coefficient matrix. TE 3 = -2t y' -2 3t = -3 6 -21 " ÿ. and X₂ 1 b. For each eigenpair in the previous part, form a solution of y'= Ay. Use t as the independent variable in your answers. and ₂(t): = -1t V2: 2t = -1 2 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
onsider the linear system A₁ = 0 v1 = ÿ₁(t) = a. Find the eigenvalues and eigenvectors for the coefficient matrix. TE 3 = -2t y' -2 3t = -3 6 -21 " ÿ. and X₂ 1 b. For each eigenpair in the previous part, form a solution of y'= Ay. Use t as the independent variable in your answers. and ₂(t): = -1t V2: 2t = -1 2 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.
= 0
, V1 =
1(t) =
=
-2t
-2
3t
v=13&v
3
y.
"
and X2
=
1
b. For each eigenpair in the previous part, form a solution of ÿ' = Aÿ. Use t as the independent variable in
your answers.
and y₂(t)
=
-1t
, V₂
2t
||
-1
2
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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