For the given matrix H in M2(R) and for any real number r let Vsubr denote the solution space in M2(R) of the equation

[xy]

[zw]H =

rH[xy]

[zw]

Find a basis for Vsub2 given that

H = [01]

[-10]

Okay. So I had some difficulty typing this question so it looks really awkward. But I think you can figure out what I'm doing. H is a 2X2 matrix.

[xy]

[zw] is supposed to be a 2x2 matrix also.

thanks.