(1 point) In this problem you will solve the nonhomogeneous system A. Write a fundamental matrix for the associated homogeneous system -2 2 y' = [3, 4] 3 + [364] -9 y 3et 2et Y = B. Compute the inverse y-¹ = C. Multiply by g and integrate 1 -¹g dt = (Do not include C1 and C2 in your answers). D. Give the solution to the system y = + +C1 +C₂ C₂ C₁+ (Do not include C1 and C2 in your answers). If you don't get this in 2 tries, you can get a hint. Hint: ⚫ The matrix -2 -9 [4] has 引 2 has (131)-eigenvector [3431] + 3i cos(ẞt) sin(ẞt) . The matrix Y = eat - sin(ẞt) cos(ẞt). has determinant det (Y) = det e2at a ⚫ This problem has been carefully designed so that integration by parts is not needed.
(1 point) In this problem you will solve the nonhomogeneous system A. Write a fundamental matrix for the associated homogeneous system -2 2 y' = [3, 4] 3 + [364] -9 y 3et 2et Y = B. Compute the inverse y-¹ = C. Multiply by g and integrate 1 -¹g dt = (Do not include C1 and C2 in your answers). D. Give the solution to the system y = + +C1 +C₂ C₂ C₁+ (Do not include C1 and C2 in your answers). If you don't get this in 2 tries, you can get a hint. Hint: ⚫ The matrix -2 -9 [4] has 引 2 has (131)-eigenvector [3431] + 3i cos(ẞt) sin(ẞt) . The matrix Y = eat - sin(ẞt) cos(ẞt). has determinant det (Y) = det e2at a ⚫ This problem has been carefully designed so that integration by parts is not needed.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 72E: Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
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![(1 point) In this problem you will solve the nonhomogeneous system
A. Write a fundamental matrix for the associated homogeneous system
-2 2
y' = [3, 4] 3 + [364]
-9
y
3et
2et
Y =
B. Compute the inverse
y-¹ =
C. Multiply by g and integrate
1
-¹g dt
=
(Do not include C1 and C2 in your answers).
D. Give the solution to the system
y =
+
+C1
+C₂
C₂
C₁+
(Do not include C1 and C2 in your answers).
If you don't get this in 2 tries, you can get a hint.
Hint:
⚫ The matrix
-2
-9
[4] has
引
2
has (131)-eigenvector
[3431]
+ 3i
cos(ẞt) sin(ẞt)
. The matrix Y =
eat
- sin(ẞt) cos(ẞt).
has determinant det (Y)
= det
e2at
a
⚫ This problem has been carefully designed so that integration by parts is not needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a558142-7770-498e-a4d7-d23af22148d0%2Ff19d29ed-e878-44d0-b7c9-d704f0d4eeef%2Flvey8cg_processed.png&w=3840&q=75)
Transcribed Image Text:(1 point) In this problem you will solve the nonhomogeneous system
A. Write a fundamental matrix for the associated homogeneous system
-2 2
y' = [3, 4] 3 + [364]
-9
y
3et
2et
Y =
B. Compute the inverse
y-¹ =
C. Multiply by g and integrate
1
-¹g dt
=
(Do not include C1 and C2 in your answers).
D. Give the solution to the system
y =
+
+C1
+C₂
C₂
C₁+
(Do not include C1 and C2 in your answers).
If you don't get this in 2 tries, you can get a hint.
Hint:
⚫ The matrix
-2
-9
[4] has
引
2
has (131)-eigenvector
[3431]
+ 3i
cos(ẞt) sin(ẞt)
. The matrix Y =
eat
- sin(ẞt) cos(ẞt).
has determinant det (Y)
= det
e2at
a
⚫ This problem has been carefully designed so that integration by parts is not needed.
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