Question

Show that:

Answer 1

\[\LARGE \left[\begin{matrix}\lambda & 1 \\ 0 & \lambda \end{matrix}\right]^n=\left[\begin{matrix}\lambda^n & n \lambda^{n-1} \\ 0 & \lambda^n\end{matrix}\right]\]

Answer 2

@ganeshie8 @dan815 @Astrophysics @ikram002p

Answer 3

Can we use induction?? it works well to me. :)

Answer 4

Show that ObamaCares

Answer 5

Maybe we could model this with a directed graph on two vertices:

so entry \(a_{i,j}\) in the matrix represents the number of paths of length one from vertex \(i\) to vertex \(j\).

Would we be allowed to use the theorem that says for an adjacency matrix \(A\), the matrix for the number of paths of length \(n\) is given by \(A^n\)?