(b) Solve 2 -1 х. 9. 2
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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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![(b) Solve
\[ \mathbf{x}' = \begin{bmatrix} 2 & -1 \\ 9 & 2 \end{bmatrix} \mathbf{x}. \]
In this problem, we are given a system of linear differential equations represented in matrix form. The vector \(\mathbf{x}\) is a function of time, and the prime symbol (\('\)) denotes the derivative with respect to time. The matrix \(\begin{bmatrix} 2 & -1 \\ 9 & 2 \end{bmatrix}\) is the coefficient matrix, and it determines how each component of \(\mathbf{x}\) changes over time. The task is to solve for \(\mathbf{x}\) as a function of time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F820a86f4-7194-4c38-bb3b-53057670e22e%2Ffd34f74b-4b2a-4a2c-94e8-154d7e312641%2Feqajfem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Solve
\[ \mathbf{x}' = \begin{bmatrix} 2 & -1 \\ 9 & 2 \end{bmatrix} \mathbf{x}. \]
In this problem, we are given a system of linear differential equations represented in matrix form. The vector \(\mathbf{x}\) is a function of time, and the prime symbol (\('\)) denotes the derivative with respect to time. The matrix \(\begin{bmatrix} 2 & -1 \\ 9 & 2 \end{bmatrix}\) is the coefficient matrix, and it determines how each component of \(\mathbf{x}\) changes over time. The task is to solve for \(\mathbf{x}\) as a function of time.
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