Find the general solution of the system x'(t) = Ax(t) for the given matrix A. A = x(t) = -1 1 0 12 1 03-1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem Statement:**

Find the general solution of the system \( \mathbf{x}'(t) = A\mathbf{x}(t) \) for the given matrix \( A \).

\[ A = \begin{bmatrix} -1 & 1 & 0 \\ 1 & 2 & 1 \\ 0 & 3 & -1 \end{bmatrix} \]

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**Solution:**

\[ \mathbf{x}(t) = \boxed{\phantom{x}} \]
Transcribed Image Text:**Problem Statement:** Find the general solution of the system \( \mathbf{x}'(t) = A\mathbf{x}(t) \) for the given matrix \( A \). \[ A = \begin{bmatrix} -1 & 1 & 0 \\ 1 & 2 & 1 \\ 0 & 3 & -1 \end{bmatrix} \] --- **Solution:** \[ \mathbf{x}(t) = \boxed{\phantom{x}} \]
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Step 1: Introduction of the given problem

x apostrophe equals A x
A equals open square brackets table row cell negative 1 end cell 1 0 row 1 2 1 row 0 3 cell negative 1 end cell end table close square brackets

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