Using Matrices to Solve System of Linear Equation (Cramer's Rule):

Matrices and their determinant can be used to solve a system of equations.  This technique becomes especially attractive while large numbers of unknowns are included. But the method is still meaningful in solving algebraic equations holding two and three unknowns.

In part one of this chapters, it was display that equations could be organized such that their coefficients could be written as a matrix.

ax + by = c

ex + fy = g

where:

x and y are variables

a, b, e, and f are the coefficients

c and g are constants

The equations can be rewritten in matrix form as given below:

To solve for each variable, the matrix will containing the constants (c,g) is substituted in place of the column containing the coefficients of the variable which we want to solve for (a,e or b,f ).  That new matrix is divided by the original coefficient matrix.  This process is known as "Cramer's Rule."