Using eigenvalues and eigenvectors, find the general solution to
dx/dt = x - y
dy/dt = x + y
Matrix 'A' - lambda*identity matrix ; for finding eigenvalues and thus eigenvectors
Other relevant equations written on the attached scanned image of my attempt at solving the question.
The Attempt at a Solution
Attached is my attempt, my lecture notes aren't clear on which eigenvalue to use when determining a general solution so at first I used the eigenvalue lambda = i + 1 which yielded a solution far from that in the answer section of this work booklet.
Using lambda = -i + 1 I got an answer very similar to the correct answer. At the bottom surrounded by a scribbled box is the answer from the book however I'm confused how they got their imaginary values...