Possible Duplicate:
Property of an operator in a finite-dimensional vector space $V$ over $R$
How do we prove the stabilization property:there exists $N$ such that for all $n \geq N$, we have $K_n=K_N$, $I_n= I_N$?
Possible Duplicate:
Property of an operator in a finite-dimensional vector space $V$ over $R$
How do we prove the stabilization property:there exists $N$ such that for all $n \geq N$, we have $K_n=K_N$, $I_n= I_N$?
Hint for (a): Note that $K_n \subseteq K_{n+1}$ and $I_{n+1} \subseteq I_n$. What can you say about the dimensions if they are not equal?