#5612: docs for solving a system of linear equations symbolically using symbolic
matrices
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Reporter: jason | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4.2
Component: linear algebra | Keywords:
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This should go into some docs somewhere. Maybe under solve_right or in a
primer?
It's to solve the linear system a*x+b*y=3, c*x+d*y=5.
{{{
sage: var('a,b,c,d,x,y')
(a, b, c, d, x, y)
sage: A=matrix(2,[a,b,c,d]); A
[a b]
[c d]
sage: result=vector([3,5]); result
(3, 5)
sage: soln=A.solve_right(result) # you could also do soln=A\result
sage: soln
(3/a - b*(5 - 3*c/a)/(a*(d - b*c/a)), (5 - 3*c/a)/(d - b*c/a))
Now, checking our answers:
sage: (a*x+b*y).subs(x=soln[0],y=soln[1]).simplify_full()
3
sage: (c*x+d*y).subs(x=soln[0],y=soln[1]).simplify_full()
5
Or just checking it with matrix multiplication:
sage: A*soln
(a*(3/a - b*(5 - 3*c/a)/(a*(d - b*c/a))) + b*(5 - 3*c/a)/(d - b*c/a),
c*(3/a - b*(5 - 3*c/a)/(a*(d - b*c/a))) + (5 - 3*c/a)*d/(d - b*c/a))
Let's simplify each entry by applying the "simplify_full" function to
each entry:
sage: (A*soln).apply_map(lambda x: x.simplify_full())
(3, 5)
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5612>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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