Thank you, but I don't understand yet..What have you tried on this problem?
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?"
Suppose D is the differentiation operator on the space of polynomials. What is D(ax^2+bx+c)? When is that 0? What about D^2(ax^2+ bx+ c)? When is that 0?
Also I forgot to say that A is Matrix n by n.What have you tried on this problem?
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?"
Suppose D is the differentiation operator on the space of polynomials. What is D(ax^2+bx+c)? When is that 0? What about D^2(ax^2+ bx+ c)? When is that 0?
Can you guide me?Think determinants
Please post EXACT wording of the problem.Is the solution group of the system A3X = 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.
Please post EXACT wording of the problem.
This is a homogeneous equation - so it is restricted.
What have you learned about solution of "homogeneous" linear equations?Is the solution group of the system A3X = 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.