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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="MatSolve"></a>
MatSolve
</h2>

Solves a linear equation.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := MatSolve (A, b);
L := MatSolve(A, b, N);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  A  </pre></td>
<td></td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  N  </pre></td>
<td>a module</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Given matrix A and vector b, the <tt> MatSolve</tt> function
finds the vector x which satisfies the matrix equation A
cdot x = b. The <tt> MatSolve</tt> function returns a list
whose first entry is x. The second of L is the null
space of A. \smallskip
If Acdot x = b has no solution, then <tt> FALSE</tt> is returned.
If the module N is given, solutions modulo N are returned.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> M := Mat(Z,[[1,0],[0,1]]);
[1 0]
[0 1]
kash> b := Mat(Z,[[1],[2]]);
[1]
[2]
kash> MatSolve(M, b);
[ [1]
    [2], Matrix with 2 rows and 0 columns ]
kash> M := Mat(Z,[[1,0,1],[0,1,1]]);
[1 0 1]
[0 1 1]
kash> MatSolve(M, b);
> [ [1]
    [2]
    [0], [ 1]
    [ 1]
    [-1] ]

</pre>

<p>


<hr>

<p>
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