Invariant means that it does not change under the transformation doesn't it? I'm guessing that you use eigenvalues and eigenvectors at some point?
Hi, another question from me again
A transformation : is represented by the matrix .
a) The two eigen values for A
b) A cartesian equation for each of the two lines passing through the origin which are invariant under .
a) This was easy enough, -4 and 6.
b) No idea how to start this, anyone got any pointers?
Yes, part b is just asking you to find the eigenvectors corresponding to the eigenvalues and then write the equations of line through the origin in the direction of those vectors. And that's easy: The fact that -4 is an eigenvalue means that there exist non-zero x, y satisfying . Multiplying that out and setting components equal immediately gives two equations that both satisfy y= -2x. That is one of the invariant lines.