# Math Help - Dimension problem

1. ## Dimension problem

Let A be an nxn matrix. Prove that $dim(span( \{ I_n ,A,A^2... \} )) \leq n$

Let A be an nxn matrix. Prove that $\dim(\text{span}( \{ I_n ,A,A^2... \} )) \leq n$
This is easy if you know the Cayley–Hamilton theorem, which tells you that A^n is a linear combination of lower powers of A.