SOLUTION: cramer rule x+2y+2z=2;x+y+z=0;x-2z=-0.4 solve this math

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Question 1069415: cramer rule
x+2y+2z=2;x+y+z=0;x-2z=-0.4
solve this math

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
x+2y+2z=2
x+y+z=0
x-2z=-4


Write in all the 1 coefficients, as well as +0y
in the third equation for the missing term in y:



Cramer's rule:
 
There are 4 columns,
 
1. The column of x-coefficients matrix%283%2C1%2C1%2C1%2C1%29
 
2. The column of y-coefficients matrix%283%2C1%2C2%2C1%2C0%29
 
3. The column of z-coefficients matrix%283%2C1%2C2%2C1%2C-2%29 
 
4. The column of constants:     red%28matrix%283%2C1%2C2%2C0%2C-0.4%29%29
 
There are four determinants:
 
1. The determinant D consists of just the three columns
of x, y, and z coefficients. in that order, but does not
contain the column of constants.
 
D=abs%28matrix%283%2C3%2C1%2C2%2C2%2C1%2C1%2C1%2C1%2C0%2C-2%29%29. 
 
It has value D=2.  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, ask me for help in the thank-you note
form below. 
 
2. The determinant D%5Bx%5D is like the determinant D
except that the column of x-coefficients is replaced by the
column of constants.  D%5Bx%5D does not contain the column 
of x-coefficients.
 
.
 
It has value D%5Bx%5D=-4.
 
3. The determinant D%5By%5D is like the determinant D
except that the column of y-coefficients is replaced by the
column of constants.  D%5By%5D does not contain the column 
of y-coefficients.
 
.
 
It has value D%5By%5D=28%2F5.
 
4. The determinant D%5Bz%5D is like the determinant D
except that the column of z-coefficients is replaced by the
column of constants.  D%5Bz%5D does not contain the column 
of z-coefficients.
 
.
 
It has value D%5Bx%5D=-8%2F5.
 
Now the formulas for x, y and z are
 
x=D%5Bx%5D%2FD=%28-4%29%2F2=-2
y=D%5By%5D%2FD=%2828%2F5%29%2F%28-2%29=%2828%2F5%29%281%2F2%29=14%2F5
x=D%5Bz%5D%2FD=%28-8%2F5%29%2F2=%28-8%2F5%29%281%2F2%29=-4%2F5
 
Solution = %28matrix%281%2C5%2Cx%2C%22%2C%22%2Cy%2C%22%2C%22%2Cz%29%29 = %28matrix%281%2C5%2C-2%2C%22%2C%22%2C14%2F5%2C%22%2C%22%2C-4%2F5%29%29

Edwin