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The Maxima on-line user's manual

Algebra Calculator

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Linsolve Calculator

Linsolve

Function: linsolve ([<expr_1>, ..., <expr_m>], [<x_1>, ..., <x_n>]) Solves the list of simultaneous linear equations for the list of variables. The expressions must each be polynomials in the variables and may be equations.

eq1:x^3+x-1=0;
linsolve([eq1],[x]);

When globalsolve is true, each solved-for variable is bound to its value in the solution of the equations.

When backsubst is false, linsolve does not carry out back substitution after the equations have been triangularized. This may be necessary in very big problems where back substitution would cause the generation of extremely large expressions.

When linsolve_params is true, linsolve also generates the %r symbols used to represent arbitrary parameters described in the manual under algsys. Otherwise, linsolve solves an under-determined system of equations with some variables expressed in terms of others.

When programmode is false, linsolve displays the solution with intermediate expression (%t) labels, and returns the list of labels.

          (%i1) e1: x + z = y;
          (%o1)                       z + x = y
          (%i2) e2: 2*a*x - y = 2*a^2;
                                                 2
          (%o2)                   2 a x - y = 2 a
          (%i3) e3: y - 2*z = 2;
          (%o3)                      y - 2 z = 2
          (%i4) [globalsolve: false, programmode: true];
          (%o4)                     [false, true]
          (%i5) linsolve ([e1, e2, e3], [x, y, z]);
          (%o5)            [x = a + 1, y = 2 a, z = a - 1]
          (%i6) [globalsolve: false, programmode: false];
          (%o6)                    [false, false]
          (%i7) linsolve ([e1, e2, e3], [x, y, z]);
          Solution

          (%t7)                       z = a - 1

          (%t8)                        y = 2 a

          (%t9)                       x = a + 1
          (%o9)                    [%t7, %t8, %t9]
          (%i9) %;
          (%o9)            [z = a - 1, y = 2 a, x = a + 1]
          (%i10) [globalsolve: true, programmode: false];
          (%o10)                    [true, false]
          (%i11) linsolve ([e1, e2, e3], [x, y, z]);
          Solution

          (%t11)                      z : a - 1

          (%t12)                       y : 2 a

          (%t13)                      x : a + 1
          (%o13)                 [%t11, %t12, %t13]
          (%i13) %;
          (%o13)           [z : a - 1, y : 2 a, x : a + 1]
          (%i14) [x, y, z];
          (%o14)                 [a + 1, 2 a, a - 1]
          (%i15) [globalsolve: true, programmode: true];
          (%o15)                    [true, true]
          (%i16) linsolve ([e1, e2, e3], [x, y, z]);
          (%o16)           [x : a + 1, y : 2 a, z : a - 1]
          (%i17) [x, y, z];
          (%o17)                 [a + 1, 2 a, a - 1]

There are also some inexact matches for linsolve. Try ?? linsolve to see them.

(%o1)                                true
(%i2) 

Linsolve Example

Related Examples

linsolve

eq1:(25-u)*(25-u)+(32...

eq2:v=r;

eq3:u=r;

Calculate

linsolve

z1:a+b/c+d+e- 26=0;

z2:f+g*h+i+j-194=0;

z3:k+l+m*n+o-122=0;

Calculate

linsolve-tex

eq1:I + ri*(ta*Ba+tp*...

eq2:O + ro*((1-ta)*Ba...

eq3:Ba = (1-ta)*O+ta*I;

Calculate

linsolve-round

eq1:gb+w1*A*rhow=R/g*...

eq2:gb+w2*A*rhow=R/g*...

eq3:w1+xl=w2+xv;

Calculate

linsolve-sqrt

eq3:x1=x*sqrt(1-y*y/2...

eq3:y1=y*sqrt(1-z*z/2...

eq3:z1=z*sqrt(1-x*x/2...

Calculate

linsolve

eq1:a+x+(5*x)=y;

linsolve([eq1],[x]);

Calculate

linsolve

eq1:x*4+y-2=y;

eq2:x+2=y;

linsolve([eq1,eq2],[x...

Calculate

linsolve

eq1:180=2*x+100*y/(10...

eq2:.150=(100+x+y)/((...

linsolve([eq1,eq2],[x...

Calculate

linsolve

eq1: x+y+z = 6;

eq2: x-y-z = 0;

eq3: 2*x +3*y +6*z = 18;

Calculate

linsolve

eq1:x1*s1+x2*s2+n*s3=D;

eq2:y1*s1+y2*s2+m*s3=D;

eq3:y1*s1+s2+m*s3=D;

Calculate