SOLUTION: Find z by the use of determinant : 3x-4y+2z+8=0, x+5y-3z+2=0, 5x+3y-z+6=0

Algebra ->  Equations -> SOLUTION: Find z by the use of determinant : 3x-4y+2z+8=0, x+5y-3z+2=0, 5x+3y-z+6=0       Log On


   

Question 865898: Find z by the use of determinant : 3x-4y+2z+8=0, x+5y-3z+2=0, 5x+3y-z+6=0
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
3x-4y+2z+8=0, x+5y-3z+2=0, 5x+3y-z+6=0

Get the constants on the right:

3x-4y+2z=-8, x+5y-3z=-2, 5x+3y-z=-6

I'll color the constants red:

system%283x-4y%2B2z=red%28-8%29%2Cx%2B5y-3z=red%28-2%29%2C5x%2B3y-z=red%28-6%29%29

D=abs%28matrix%283%2C3%2C%0D%0A3%2C-4%2C+2%2C%0D%0A1%2C+5%2C+-3%2C%0D%0A5%2C+3%2C+-1%29%29 

x is the FIRST unknown and so D%5Bx%5D is just like D
except that the FIRST column is replaced by the three red numbers: 



y is the SECOND unknown and so D%5By%5D is just like D
except that the SECOND column is replaced by the three red numbers: 




z is the THIRD unknown and so D%5Bz%5D is just like D
except that the THIRD column is replaced by the three red numbers,



Do you know how to evaluate a 3x3 determinant?
If not, post again asking how to.  I will assume
you already know how.

D=24
D%5Bx%5D=-48
D%5By%5D=72
D%5Bz%5D=120

Then the solutions are:

x=D%5Bx%5D%2FD=%28-48%29%2F24+=+-2
y=D%5By%5D%2FD=%2872%29%2F24+=+3
z=D%5Bz%5D%2FD=%28120%29%2F24+=+5

Edwin