Specific Question:
Let $M=(1/53)⋅[[45, 28], [28,-45]]$. M is the matrix of the reflection about a line. Find a vector v of magnitude (53)^0.5 parallel to that line.
Currently in class we are dealing with eigenvalues and eigenvectors. From the matrix M I found the Eigenvalues to be 53 and -53. I then used the equation MU=UD, and then simplified it to get Det(M-/lambda*I)*U=0. Using that equation I was able to get my eigenvectors which are [[98, 28],[28, 8]]. I was able to find an answer by finding the lowest common denominator of the first row of the matrix I just found. This would be [7,2].
I was able to find an answer on the homework problems by just looking for a pattern in the problem and answer sets. However, I really am not sure what I did, or whether its a valid solution or not.