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
To find: (a) = Write system in matrix form , find eigenvalues and eigenvectors.
(b). = General solution.
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:
Simplify all fractions!