a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they will be complex valued)

b) Write down the general solution for the system of differential equations using only real valued functions. [Hint : use the equality

foass77W
2021-09-10
Answered

Consider the system $\dot{x}=x-y,\dot{y}=x+y$

a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they will be complex valued)

b) Write down the general solution for the system of differential equations using only real valued functions. [Hint : use the equality${e}^{i\omega t}=\mathrm{cos}\left(\omega t\right)+i\mathrm{sin}\left(\omega t\right)$ ]

a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they will be complex valued)

b) Write down the general solution for the system of differential equations using only real valued functions. [Hint : use the equality

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hosentak

Answered 2021-09-11
Author has **100** answers

Step 1

Given:

To find: (a) = Write system in matrix form , find eigenvalues and eigenvectors.

(b). = General solution.

Step 2.

Solution: a)

Required matrix form of the system.

Eigenvalues of matrix A :

Hence the eigenvalues are in complex from which are 1+i , 1-i

Eigenvector corresponding to 1+i :

Eigenvector corresponding to 1-i:

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