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## Homework Statement

Using eigenvalues and eigenvectors, find the general solution to

dx/dt = x - y

dy/dt = x + y

## Homework Equations

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...