Let A=[[|gathered 2 1 2 6 2 11 3 3 2 gathered]]| and P=[[|gathered 1 2 0 5 0 2 7 1 5 gathe…

Question

Let $A=[[|\begin{gathered} 2 \quad  1 \quad  2 \ 6 \quad  2 \quad  11 \ 3 \quad  3 \quad  2 \end{gathered}]]|$ and $P=[[|\begin{gathered} 1 \quad  2 \quad  0 \ 5 \quad  0 \quad  2 \ 7 \quad  1 \quad  5 \end{gathered}]]|$. The sum of the prime factors of $|{P}^{-1}AP-2I|$ is equal to

Accepted Answer

$\begin{gathered} |{P}^{-1}AP-2I| \quad  =|{P}^{-1}AP-2{P}^{-1}P| \ =|{P}^{-1}(A-2I)P| \ =|{P}^{-1}||A-2I||P| \ =|A-2I| \ =|\begin{array}{ccc}0 \quad  1 \quad  2 \ 6 \quad  0 \quad  11 \ 3 \quad  3 \quad  0\end{array}|=69 \end{gathered}$

So, Prime factor of 69 is 3 \& 23

So, sum = 26

Solutions · 1