[VA] SRC#003- New Year 2019 Special

[Thomas Klemm]

(01-16-2019 04:24 AM)Thomas Okken Wrote:  

Code:


SPOILERS!!!













Trying the exercise with a 4x4 matrix and looking at the top two elements
of the 4th column, the ratio converges to the 4th root of 2019. I bet
there's a pattern there, and it has something to do with the eigenvalues
of M...

A similar calculation can be done:

\(\begin{bmatrix}
a & u^4 & u^4 & u^4\\
1 & a & u^4 & u^4\\
1 & 1 & a & u^4\\
1 & 1 & 1 & a
\end{bmatrix}
\begin{bmatrix}
u^3\\
u^2\\
u\\
1
\end{bmatrix}=
\begin{bmatrix}
au^3+u^6+u^5+u^4\\
u^3+au^2+u^5+u^4\\
u^3+u^2+au+u^4\\
u^3+u^2+u+a
\end{bmatrix}=
(u^3+u^2+u+a)
\begin{bmatrix}
u^3\\
u^2\\
u\\
1
\end{bmatrix}\)

Cheers
Thomas