Let v (t) = [€ 0 -30-21], $(t) = [ 30-2 1] -9e-2t a. Verify that the matrix (t) is a fundamental matrix of the given linear system. b. Determine a constant matrix C such that the given matrix Î(t) can be represented as Î(t) = V(t)C. c. The determinant of the matrix C is simply a solution matrix _175₁ ÿ, C = " which is zero Therefore, the matrix (t) is
Let v (t) = [€ 0 -30-21], $(t) = [ 30-2 1] -9e-2t a. Verify that the matrix (t) is a fundamental matrix of the given linear system. b. Determine a constant matrix C such that the given matrix Î(t) can be represented as Î(t) = V(t)C. c. The determinant of the matrix C is simply a solution matrix _175₁ ÿ, C = " which is zero Therefore, the matrix (t) is
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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please solve it on paper
![Let
y (t) - [e
c. The determinant of the matrix C is
simply a solution matrix
с
1
ÿ' = [_25₁
ÿ,
0-2
=
e
1-2)], * (1) = [
-3e-2t
a. Verify that the matrix (t) is a fundamental matrix of the given linear system.
b. Determine a constant matrix C such that the given matrix (t) can be represented as Î(t) = ¥(t)C.
"
which is
3e-2t
-9e
-2t
zero
:]
Therefore, the matrix Î (t) is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05295cc1-71f0-4e3b-b6f8-2c1731c6d617%2F292af02c-4ab7-4aab-90a8-a60f90fa00b6%2Frefeykj_processed.png&w=3840&q=75)
Transcribed Image Text:Let
y (t) - [e
c. The determinant of the matrix C is
simply a solution matrix
с
1
ÿ' = [_25₁
ÿ,
0-2
=
e
1-2)], * (1) = [
-3e-2t
a. Verify that the matrix (t) is a fundamental matrix of the given linear system.
b. Determine a constant matrix C such that the given matrix (t) can be represented as Î(t) = ¥(t)C.
"
which is
3e-2t
-9e
-2t
zero
:]
Therefore, the matrix Î (t) is
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