Please help me prove this

  • Thread starter Hala91
  • Start date
  • #1
9
0
please help me prove this....

Homework Statement



Show that If "A" is an n-rowed matrix that satisfies A^2=A Then:
Row(A)+Row(I-A)=n

Homework Equations





The Attempt at a Solution


well since A is n-rowed that means that its an n*n matrix so Ax=I
as i guess so :
Row(A)=Rank(A)
Rank(I-A)+nullity(I-A)=Rank(A)+nullity(A)=n
plz help if i find its solution I will be given 20 mark for it and i have been trying to solve it for over two day :S
 

Answers and Replies

  • #2
hunt_mat
Homework Helper
1,749
27


Examining the eigenvales might help, note that:
[tex]
Ax=\lambda x\Rightarrow A^{2}x=\lambda Ax\Rightarrow Ax=\lambda^{2}x
[/tex]
I am not too sure what you mean by Row(A)
 
  • #3
12
0


Multiply
[tex]A (I-A)[/tex] and solve it. what does that tell you?
 
  • #4
9
0


Thanks A lot guys I have proved it with your help :)
 

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