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 .
Find:
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?
Thanks
It means that points on that line are mapped into points on that line. For eigenvectors, v, [tex]Av= \lamba v[/itex] and, interpreting v as position vector that means Av points in the same direction as v: They lie on the same line as v.
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.