View source for Tutorial:JMathLab/Equations (Linear Systems)


= Systems of Linear Equations =

Solving systems of linear equations is accomplished by either the function
'''linsolve(A,b)''', or '''linsolve2(A,b)''' (LAPACK). In both cases A is the quadratic matrix of the system of
equations, and b a (row or column) vector representing the right-hand-side of
the equations. The equations may be written as $A\cdot z = b$ and we solve for
$z$.

<jc lang="math">
A=[2 3 1; 4 4 5; 2 9 3];
b=[0;3;1];
a=linsolve(A,b)
printf('%f\n',a)
 
% a=linsolve2(A,b) % for JLAPAC
% printf('%f\n',a)
</jc>

For large numeric matrices one should use the LAPACK-version if available. The
Jasymca version can also handle matrices containing exact or symbolic
elements. To avoid rounding errors in these cases it is advisable to work with
exact numbers if possible:

<jc lang="math">
syms x,y
A=[x,1,-2,-2,0;1 2 3*y 4 5;1 2 2 0 1;9 1 6 0 -1;0 0 1 0] 
printf('%f\n',A)  
b = [1 -2  3  2  4 ];
a=trigrat( linsolve( rat(A), b) )  
printf('%f\n',a)
</jc>