How to Write a Linear System in Matrix Form

Thread starter Totalderiv
Start date Mar 5, 2012
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Linear Matrices Systems

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To write the given system of equations x' = -3y and y' = 3x in matrix form, it can be expressed as x' = P(t)x + f(t). The matrix P(t) can be constructed from the coefficients of the variables in the system, leading to a representation of the form x' = A x, where A is the coefficient matrix. The discussion highlights a lack of examples in the textbook and class notes, prompting a request for guidance on how to approach this problem. Understanding the structure of the matrix and the role of the function f(t) is crucial for solving the system. Clarifying these concepts will aid in successfully writing the linear system in matrix form.

Mar 5, 2012

Totalderiv

Homework Statement

Write the given system in the form x'=P(t)x + f(t)

x'=-3y , y'=3x

Homework Equations

x'=P(t)x + f(t)
x(t)=c_1x_1(t)+c_2x_2(t)+...+c_nx_n(t)

The Attempt at a Solution

I have no idea how to start this since my teacher never covered this in our notes and the book doesn't give an example of this type of problem. Please help!

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Mar 8, 2012

Totalderiv

Any one?

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