Let A be a 2 x 2 diagonalizable matrix. 3et+ ecit If is the solution to the system ở' (t) = Ax(t), 3e²t + ec₂t then check All the possible values of c₁ and c₂ below. (a)c₁ = 1; (b) C₁ = 2; (c) C₁ = 3; (d) c₂ = = 1; (e) c₂ = 2; (f) C₂ (a) (b) (c) (d) (e) (f) U 1 U U = 3.
Let A be a 2 x 2 diagonalizable matrix. 3et+ ecit If is the solution to the system ở' (t) = Ax(t), 3e²t + ec₂t then check All the possible values of c₁ and c₂ below. (a)c₁ = 1; (b) C₁ = 2; (c) C₁ = 3; (d) c₂ = = 1; (e) c₂ = 2; (f) C₂ (a) (b) (c) (d) (e) (f) U 1 U U = 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement**
Let \( A \) be a \(2 \times 2\) diagonalizable matrix.
If
\[
\left[
\begin{array}{c}
3e^t + e^{c_1 t} \\
3e^{2t} + e^{c_2 t}
\end{array}
\right]
\]
is the solution to the system \(\vec{x}'(t) = A \vec{x}(t)\),
then check all the possible values of \( c_1 \) and \( c_2 \) below:
- (a) \( c_1 = 1 \)
- (b) \( c_1 = 2 \)
- (c) \( c_1 = 3 \)
- (d) \( c_2 = 1 \)
- (e) \( c_2 = 2 \)
- (f) \( c_2 = 3 \)
**Options:**
- ☐ (a)
- ☐ (b)
- ☐ (c)
- ☐ (d)
- ☐ (e)
- ☐ (f)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F238584dd-2c47-447e-aaba-b9fce1ec1b5c%2Fd2375b8f-c09a-4668-b916-f7ef36cbc783%2Flwz5zmf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Let \( A \) be a \(2 \times 2\) diagonalizable matrix.
If
\[
\left[
\begin{array}{c}
3e^t + e^{c_1 t} \\
3e^{2t} + e^{c_2 t}
\end{array}
\right]
\]
is the solution to the system \(\vec{x}'(t) = A \vec{x}(t)\),
then check all the possible values of \( c_1 \) and \( c_2 \) below:
- (a) \( c_1 = 1 \)
- (b) \( c_1 = 2 \)
- (c) \( c_1 = 3 \)
- (d) \( c_2 = 1 \)
- (e) \( c_2 = 2 \)
- (f) \( c_2 = 3 \)
**Options:**
- ☐ (a)
- ☐ (b)
- ☐ (c)
- ☐ (d)
- ☐ (e)
- ☐ (f)
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