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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
It is the last case that we require to take a look at. During this section we are going to look at solutions to the system, x?' = A x? Here the eigenvalues are repeated eigen
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It's now time to do solving systems of differential equations. We've noticed that solutions to the system, x?' = A x? It will be the form of, x? = ?h e l t Here l and
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