Math Solutions

[Solution Library] Invertibility of population dynamics matrix. Consider the population dynamics matrix

Question: Invertibility of population dynamics matrix. Consider the population dynamics matrix

\[A=\left[\begin{array}{ccccc} b_{1} & b_{2} & \cdots & b_{99} & b_{100} \\ 1-d_{1} & 0 & \cdots & 0 & 0 \\ 0 & 1-d_{2} & \cdots & 0 & 0 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & \cdots & 1-d_{99} & 0 \end{array}\right]\]

where \(b_{i} \geq 0\) are the birth rates and \(0 \leq d_{i} \leq 1\) are death rates. What are the conditions on \(b_{i}\) and \(d_{i}\) under which \(A\) is invertible? (If the matrix is never invertible or always invertible, say so.) Justify your answer.

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


∴ Other downloads you may be interested in ∴

log in to your account

Forgot password?
Don't have a membership account?
REGISTER

reset password

Back to
log in

sign up

Back to
log in