Solving Systems of Equations

Consider the set of equations

x + 2y + z + t = a

-x + 4y - 2z = b

x + 3y + 4z + 5t = c

x + z + t = d

We illustrate how to use a matrix representation to write these out and solve them…

Start with the matrix of coefficients of the variables, mymatrix:

The system of equations will only have a unique solution if the determinant of mymatrix is nonzero.

The left-hand side of the first equation will be

and the left-hand side of all four equations will be

Now define an indexed variable linsys with four entries, each being one of the equations in the system of interest:

Solving the set of equations for the unknowns

Created by Wolfram Mathematica 6.0 (06 September 2007) |