Răspuns:
Explicație pas cu pas:
1)
[tex]\begin{matrix} a & b & c\\0 & a & d\\0 & 0 & a\end{matrix}\\a, b, c, d = 0 =>\\\begin{matrix}\\0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix} = O_3 \in M[/tex]
2)
[tex]M_1, M_2 \in M[/tex]
[tex]M_n \in M\\a_n, b_n, c_n, d_n \in R\\\\M_n = \begin{matrix}a_n & b_n & c_n\\0& a_n & d_n\\0 & 0 & a_n \end{matrix}\\M_n M_m = \begin{matrix}a_n a_m & a_n b_m + b_na_m & a_n c_m + b_n d_m + c_n a_m \\ 0 & a_n a_m & a_n d_m + d_n a_m\\ 0 & 0 & a_n a_m \end{matrix}\\a_n, b_n, c_n, d_n \in R => xa_n + yb_n + zc_n \in R, x, y, z \in R[/tex]
Restul nu am timp sa le rezolv.
