SOLUTION: 2x-y+8z=13;3x+4y+5z=18;5x-2y+7z=20; x= y= z= solve the following equations through gauss jordan method

Algebra ->  Matrices-and-determiminant -> SOLUTION: 2x-y+8z=13;3x+4y+5z=18;5x-2y+7z=20; x= y= z= solve the following equations through gauss jordan method       Log On


   

Question 630512: 2x-y+8z=13;3x+4y+5z=18;5x-2y+7z=20;
x=
y=
z=
solve the following equations through gauss jordan method
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Initial matrix
       2      -1       8      13
       3       4       5      18
       5      -2       7      20

Row 1 = Row 1 times 1/2
       1    -1/2       4    13/2
       3       4       5      18
       5      -2       7      20

Row 2 = row 2 + -3 times row 1
       1    -1/2       4    13/2
       0    11/2      -7    -3/2
       5      -2       7      20

Row 3 = row 3 + -5 times row 1
       1    -1/2       4    13/2
       0    11/2      -7    -3/2
       0     1/2     -13   -25/2

Row 2 = Row 2 times 2/11
       1    -1/2       4    13/2
       0       1  -14/11   -3/11
       0     1/2     -13   -25/2

Row 1 = row 1 + (1/2) times row 2
       1       0   37/11   70/11
       0       1  -14/11   -3/11
       0     1/2     -13   -25/2

Row 3 = row 3 + (-1/2) times row 2
       1       0   37/11   70/11
       0       1  -14/11   -3/11
       0       0 -136/11 -136/11

Row 3 = Row 3 times -11/136
       1       0   37/11   70/11
       0       1  -14/11   -3/11
       0       0       1       1

Row 1 = row 1 + (-37/11) times row 3
       1       0       0       3
       0       1  -14/11   -3/11
       0       0       1       1

Row 2 = row 2 + (14/11) times row 3
       1       0       0       3
       0       1       0       1
       0       0       1       1

So x = 3, y = 1 and z = 1 (from the last column).