Converting system of equations to form Ax=b

Hi,

I have the following system of equations:

- t + w + x = 100 eq(1)

t - u = 100 eq(2)

v + w - y - z = 0 eq(3)

u + v = 40 eq(4)

Suppose I have t = 100 and w + y+ z = 100, then I want to write this system of equations in the form Ax = b.

This is how I tried to do it:

eq(1): -100 + w + x = 100

=> w + x = 200

eq(2): t - u = 100

=> 100 - u = 100

=> u = 0

eq(3): v + w - y - z = 0

=> v + w- (y+z) = 0

=> v + w - (100 - w) = 0

=> v + 2w = 100

eq(4): u + v = 40

If I put u = 0 of eq(2) in it, I get:

v = 40

If I put v=40 in eq(3), I get:

w = 30

If I put it w=30 in eq(1), I get:

x = 170

I am stuck here. I am just not understanding what to do next to convert this all in system Ax=b. I am not sure even if I have done it in correct way. Can you please guide me in this all? Any help will be highly appreciated.

Answer 1

[John D'Errico]

help equationsToMatrix

--- help for sym/equationsToMatrix ---

 equationsToMatrix  Convert linear equations to matrix notation.
    [A,b] = equationsToMatrix([eq1,eq2,eq3,...],[x1,x2,...,xn]) converts 
    the equations eq1,eq2,eq3,... to matrix notation. Equations need to be
    linear in the variables specified as second argument. eq1,eq2,eq3,...
    can be SYM equations or simply SYM objects. In case eq1,eq2,eq3,... 
    are generic SYM objects, they will be interpreted as left sides 
    of equations, whose right sides are equal to 0. The equations just
    need to be linear in the given variables, it does not play a role how 
    they are ordered or on which side of the equations the unknowns show up. 
 
    [A,b] = equationsToMatrix([eq1,eq2,eq3,...]) converts the equations 
    [eq1,eq2,eq3,...] to matrix notation. Equations need to be linear in
    all variables of the equations. The system is interpreted as a linear 
    system of equations in the variables symvar([eq1,eq2,eq3,...]).
 
    [A,b] = equationsToMatrix(eq1,eq2,eq3,...,x1,x2,...,xn) does the same 
    as equationsToMatrix([eq1,eq2,eq3,...],[x1,x2,...,xn]). 
   
    [A,b] = equationsToMatrix(eq1,eq2,eq3,...) does the same as 
    equationsToMatrix([eq1,eq2,eq3,...]). 
 
    If you do not assign the output to variables A and b or just assign the 
    output to a single variable, only the matrix A will be returned.  
 
    Examples: 
 
    syms x y z
    eq1 = x + y + z
    eq2 = x - 2*y - 5*z == 0
    eq3 = x - z == 1
   
    [A,B] = equationsToMatrix([eq1,eq2,eq3],[x,y,z])
    A = equationsToMatrix([eq1,eq2,eq3],[x,y,z])
    [A,B] = equationsToMatrix(eq1,eq2,eq3,x,y,z)
    A = equationsToMatrix(eq1,eq2,eq3,x,y,z)
    [A,B] = equationsToMatrix([eq1,eq2,eq3])
    A = equationsToMatrix([eq1,eq2,eq3])
    [A,B] = equationsToMatrix(eq1,eq2,eq3)
    A = equationsToMatrix(eq1,eq2,eq3)
 
    See also LINSOLVE, MLDIVIDE, SYM/LINSOLVE, SYM/MLDIVIDE, SOLVE, DSOLVE

    Documentation for sym/equationsToMatrix
       doc sym/equationsToMatrix

For example.

syms x y
E1 = x + y == 1

E1 = 

E2 = x - y == 2

E2 = 

[A,B] = equationsToMatrix(E1,E2,[x,y])

A = 

B = 

[aliza mustafa]

This is such a great help. Thank you soo much.