Chapter4: Systems Of Linear Equations
Section4.6: Solve Systems Of Equations Using Determinants
Problem 279E: Explain the steps for solving a system of equations using Cramer’s rule.
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![**Problem: General Solution of a System of Differential Equations**
Find a general solution of the system:
\[
\vec{x}' = \begin{bmatrix} 2 & -4 \\ 2 & -2 \end{bmatrix} \vec{x}
\]
**Explanation:**
This represents a system of linear differential equations involving the vector \(\vec{x}\) and a constant coefficient matrix. The objective is to determine the general form of \(\vec{x}(t)\) that satisfies this differential equation. To solve it, we typically find the eigenvalues and eigenvectors of the matrix, which will help in constructing the solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4367a19-3774-4d20-9400-fb2721047786%2Ff7899af1-6997-4c0e-ab7e-e7ff42b3e30e%2Fry7nk6i_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: General Solution of a System of Differential Equations**
Find a general solution of the system:
\[
\vec{x}' = \begin{bmatrix} 2 & -4 \\ 2 & -2 \end{bmatrix} \vec{x}
\]
**Explanation:**
This represents a system of linear differential equations involving the vector \(\vec{x}\) and a constant coefficient matrix. The objective is to determine the general form of \(\vec{x}(t)\) that satisfies this differential equation. To solve it, we typically find the eigenvalues and eigenvectors of the matrix, which will help in constructing the solutions.
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