Quiz 2: Logs/Exponentials–algebraic formulas, simplification, graphing. Give an example of an initial value problem with multiple solutions. Give an example of an initial value problem which has no solution. What conditions guarantees that an initial value problem has a solution which is unique? Are these conditions necessary for an initial value problem to have a solution which is unique? Define stable, unstable, semi-stable equilibrium solutions. The ”vectors” b_{1}, ..., b_{n} are linearly independent if .... Give examples of linearly independent vectors:

Determine if the following vectors are linearly independent:

A function f is linear if .... Give examples of linear functions:

Determine if the following functions are linear: