Consider the matrix \(A=\begin{bmatrix} -3 & 0 & 20\\ 1 & -3…

Consider the matrix \(A=\begin{bmatrix} -3 & 0 & 20\\ 1 & -3 & 1\\ 0 & 0 & 2\end{bmatrix}\). whose characteristic polynomial is given by \(p(\lambda)=(\lambda+3)^2(\lambda-2).\)Note: You do not need to find this characteristic polynomial. It is given to you above.Answer each of the following:Use this characteristic polynomial to find all eigenvalues of the matrix $A$.Find a basis for the eigenspace corresponding to each of the eigenvalues of $A$, indicating which basis corresponds to each eigenvalue.Is the matrix $A$ diagonalizable?

Imagine a divide the dollar game in which John and Jane are…

Imagine a divide the dollar game in which John and Jane are trying to reach a settlement to share $100.  They get one opportunity (that consists of a single proposal by one of them and either acceptance or rejection of that proposal by the other) to reach such a deal.  If they fail to reach a deal, the $100 disappears.  They initially flip a coin to determine who will make the first offer.  If it lands on heads, John can choose to make the first proposal or allow Jane to make the first proposal.  If it lands on tails, Jane can choose to make the first proposal or allow John to make the first proposal.  Which of the following is the most likely equilibrium outcome of this interaction if the coin flip lands on heads and both players are trying to maximize their income?

A collective security organization differs from an alliance…

A collective security organization differs from an alliance in that collective security organizations generally do not target a specific state as a security threat.  Instead, collective security organizations try to activate a generalized commitment on the part of its members to deter all aggression against them.