Author: Anonymous

Identify which one of the following sets of vectors in \(\mathbb{R}^3\) is linearly independent.

Identify which of the following vectors is orthogonal to \(\vec{u}=(2, 0, 3, 1)\).

An \(n\times n\) matrix \(A\) is diagonalizable if and only if…

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 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 preterm infant receiving chronic furosemide therapy develops hypochloremia and metabolic alkalosis. Which pharmacologic effect most likely contributed?

Match each of the following tests associated with common morality with its key criteria of application.

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.

Structural elements of the international system (like the Non-Proliferation Treaty) ______ behavior by raising the costs for some foreign policy action.

In “Beware the Europe You Wish For,” Celeste Wallander argues the United States benefits from membership in NATO in which of the following ways: