If Ax= 0 then certainly A^3x=A^2(Ax)= A^2(0)= 0 for A any linear operator. So the solution set of A is a subset of the solution set of A^3. The question is "are there x that satisfy A^3x= 0 but not Ax= 0?
Can you help me more, I need it for tomorrow :(
I wrote:
"system group of ##A x = 0 ## are not equal to system group of ##A^3 x = 0##"
I wrote it down, but I do not know if my counter-argument is true there, or if I am wrong.
Summary:: need help with solution group of Homogeneous system
Is the solution group of the system A^3X = 0
, Is equal to the solution group of the system AX = 0
If this is true you will prove it, if not give a counterexample.
thank you.