I have the matrix H:
I need to show that the equation x^2=-1 has infinitely many solutions in H.
I ignored a (because the book told me to) and so I have the matrix:
I'm just having trouble showing the "infinitely many solutions in H" part.
How does this relate back to the matrix though?
Could someone just explain this subtle point?
Your matrix is defined by the values b, c, and d by the A11, A12, A21, and A22 relations that you gave in your initial post. The condition that any matrix belonging to the set H be such that x^2 = -1 gives a constraint on the possibilities that b, c, and d can take, but is not so resistrictive as to give a finite set of possibilities.
Originally Posted by JoeDardeno23