What Happens to Av^j When j Exceeds Rank r in SVD?

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Let A be an m × n matrix of rank r and let A = U\SigmaV be an SVD of A. Prove that

Av^{j}= sigma^j* u^{j} for 1<=j<=r

What is Av^j for r + 1<=j<=n?
 
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Well, what do you think?
 
I don't know, that's why I am asking
 
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I really don't
 

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