Miklos Schweitzer 1950_4
Source: second part of 1950
October 3, 2008
linear algebramatrixlimitvectorlinear algebra unsolved
Problem Statement
Put
M\equal{}\begin{pmatrix}p&q&r\\
r&p&q\\q&r&p\end{pmatrix}
where and p\plus{}q\plus{}r\equal{}1. Prove that
\lim_{n\rightarrow \infty}M^n\equal{}\begin{bmatrix}\frac13&\frac13&\frac13\\
\frac13&\frac13&\frac13\\\frac13&\frac13&\frac13\end{bmatrix}