MATRICES AND DETERMINANTS
Higher Concepts of Mathematics
The equations can be rewritten in matrix form as follows:
a b
e f
x
y
c
g
To solve for each variable, the matrix containing the constants (c,g) is substituted in place of the
column containing the coefficients of the variable that we want to solve for (a,e or b,f ). This
new matrix is divided by the original coefficient matrix. This process is call "Cramer’s Rule."
Example:
In the above problem to solve for x,
c b
g f
x =
c b
g f
and to solve for y,
a c
e g
y =
a b
e f
Example:
Solve the following two equations:
x + 2y = 4
-x + 3y = 1
MA-05
Page 26
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