====== Math 445 HW5  ======

Main concept for this homework: the ''for'' loop.

1. Write a function ''mymean'' that uses a ''for'' loop to compute the mean of the elements of its input vector, according to the formula

\begin{eqnarray*}
\text{mean}(x) = \frac{1}{N} \sum_{i=1}^N x_i
\end{eqnarray*}

where N is the number of elements in the vector. Test that your code is correct by comparing to Matlab's built-in ''mean'' function on a random vector. 

2. Write a function ''mystd'' that uses a ''for'' loop to computes the standard deviation of the elements of its input vector. 
\begin{eqnarray*}
\text{std dev}(x) = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \bar{x})^2
\end{eqnarray*}
where $\bar{x}$ is the mean of $x$. Test by comparison to Matlab's built-in ''std'' function on a random vector.

3. Write a script that produces a 10 x 10 multiplication table whose first three lines are 

<code>
  1   2   3   4   5   6   7   8   9  10
  2   4   6   8  10  12  14  16  18  20
  3   6   9  12  15  18  21  24  27  30
  .
  .
  .
 </code>

Try to get the output in **exactly** this form.

4. Write a function ''y = matvecmult(A,x)'' that uses nested ''for'' loops to compute the matrix-vector product 
//y = Ax// according to the formula

\begin{eqnarray*}
y_i = \sum_{j=1}^N A_{ij} x_j
\end{eqnarray*}

where //N// is the number of columns of //A//. Be sure to check for compatibility between //A// and //x//. For an //M x N// matrix //A//, //x// must be an //N//-dimensional column vector, and //y// will be an //M//-dimensional column vector. If //A// and //x// do not have compatible dimensions, print an error message and return //0//-dimensional vector (a null vector).

5. Write a function ''C = matmatmult(A,B)'' that uses nested ''for'' loops to compute the matrix-vector product 
//C=AB// according to the formula

\begin{eqnarray*}
C_{ij} = \sum_{k=1}^N A_{ik} C_{kj}
\end{eqnarray*}

where //N// is the number of columns of //A//. If A is //M x N// and //B// is //N x P//, then //C// is //M x P//. If //A// and //B// do not have compatible dimensions, print an error message and return a //0 x 0// matrix.