Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Give an integer n≥2, let M(n) be the n×n matrix defined as follows, where Mᵢⱼ(n) denotes the entry in row i, column j of M(n):
[tex] \rm M_{ij}(n)=\begin{cases} \bigg( \rm \dfrac{j}{j - 1} \bigg)^{2} & \rm if \: i = j + 1 \: and \: j > 1\\& \rm 1 \: if \:i = 2 \: and \: j = 1 \\ & \rm0 \: otherwise\end{cases}[/tex]
Define matrix A(n) as follows:
[tex] \rm A(n) = \sum_{k = 0}^{ \infty } (M (n))^k \\ [/tex]

Sagot :