(Solved):   1.) Find a matrix \( P \) which tranform the following matrices to diagonal forma. Hence c ...

 

1.) Find a matrix \( P \) which tranform the following matrices to diagonal forma. Hence calculate the pover matrix. i) If \( A=\left[\begin{array}{ccc}2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2\end{array}\right] \) calculate \( A^{6} \) ii) If \( A=\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 2 & 1 \\ -4 & 4 & 3\end{array}\right] \) celculate \( A 8 \) (iii) If \( A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right] \) then show that, \( A^{n}=A^{n-2}+A^{2}-I \) for \( n \geqslant 3 \) Hence find \( A^{50} \),