1.4.17 Matrix Transformations

Condition: Find your own values and own vectors of the linear operator set by the matrix \ (A \). To prove that this is an operator of a simple type, to bring his matrix to the diagonal form (find a matrix of the transition to its own basis and do a check). Calculate \ (a^{n} \) for any \ (n \ in \ mathbb {n} \). \ [A = \ Left (\ Begin {Array} {ll} -4 & 5 \\ -1 & 2 \ End {Array} \ Right) \]