3x + 2y + z = 5
2x + 3y + z = 1
2x + y + 3z = 11
solve using cramers rule
Write in all the 1 and -1 coefficients:
Cramer's rule:
There are 4 columns,
1. The column of x-coefficients 
2. The column of y-coefficients 
3. The column of z-coefficients 
4. The column of constants: 
There are four determinants:
1. The determinant 
consists of just the three columns
of x, y, and z coefficients. in that order, but does not
contain the column of constants.
.
It has value 
. I'm assuming you know how to find the
value of a 3x3 determinant, for that's a subject all by itself.
If you don't know how, post again asking how.
2. The determinant 
is like the determinant
except that the column of x-coefficients is replaced by the
column of constants. does not contain the column
of x-coefficients.
.
It has value 
.
3. The determinant 
is like the determinant
except that the column of y-coefficients is replaced by the
column of constants. does not contain the column
of y-coefficients.
.
It has value 
.
4. The determinant 
is like the determinant
except that the column of z-coefficients is replaced by the
column of constants. does not contain the column
of z-coefficients.
.
It has value 
.
Now the formulas for x, y and z are
Edwin
