Question 891216: additional assistance requested in understanding how to get a solution
solve the system linear equations using the Gauss-Jordam method
3x + 3y + z = 22
x + z = 6
4y + 3z = 8
2x + 5y - 2z = 14
5x - 6y + 2z = 0
4x - y + 3z = -7
x - 2y = 8
3x+ 4y = 4
3x + 2y = 14
x - 4y = -14
7x + 5y = 32
-3x + y = 20
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Against my better judgement, I will do two for you.
3x + 3y + z = 22
x + z = 6
4y + 3z = 8
3,3,1,22
1,0,1,6
0,4,3,8
divide row 1 by 3/1
1,1,1/3,22/3
1,0,1,6
0,4,3,8
add down (-1/1) *row 1 to row 2
1,1,1/3,22/3
0,-1,2/3,-4/3
0,4,3,8
add down (0/1) *row 1 to row 3
1,1,1/3,22/3
0,-1,2/3,-4/3
0,4,3,8
divide row 2 by -1/1
1,1,1/3,22/3
0,1,2/-3,-4/-3
0,4,3,8
add down (-4/1) *row 2 to row 3
1,1,1/3,22/3
0,1,2/-3,4/3
0,0,-17/-3,8/3
divide row 3 by 17/3
1,1,1/3,22/3
0,1,2/-3,4/3
0,0,1,24/51
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-2/-3) *row 3 to row 2
1,1,1/3,22/3
0,1,0,-252/-153
0,0,1,8/17
add up (-1/3) *row 3 to row 1
1,1,0,1098/153
0,1,0,28/17
0,0,1,8/17
add up (-1/1) *row 2 to row 1
1,0,0,1598/289
0,1,0,28/17
0,0,1,8/17
final
1,0,0,94/17 = 5.52941176
0,1,0,28/17 = 1.64705882
0,0,1,8/17 = 0.47058824
"94/17","28/17","8/17"
next one
2x + 5y - 2z = 14
5x - 6y + 2z = 0
4x - y + 3z = -7
2,5,-2,14
5,-6,2,0
4,-1,3,-7
divide row 1 by 2/1
1,5/2,-1,7
5,-6,2,0
4,-1,3,-7
add down (-5/1) *row 1 to row 2
1,5/2,-1,7
0,-37/2,7,-35
4,-1,3,-7
add down (-4/1) *row 1 to row 3
1,5/2,-1,7
0,-37/2,7,-35
0,-11,7,-35
divide row 2 by -37/2
1,5/2,-1,7
0,1,14/-37,-70/-37
0,-11,7,-35
add down (11/1) *row 2 to row 3
1,5/2,-1,7
0,1,14/-37,70/37
0,0,-105/-37,-525/37
divide row 3 by 105/37
1,5/2,-1,7
0,1,14/-37,70/37
0,0,1,-5
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-14/-37) *row 3 to row 2
1,5/2,-1,7
0,1,0,0
0,0,1,-5
add up (1/1) *row 3 to row 1
1,5/2,0,2
0,1,0,0
0,0,1,-5
add up (-5/2) *row 2 to row 1
1,0,0,2
0,1,0,0
0,0,1,-5
final
1,0,0,2
0,1,0,0
0,0,1,-5
(2,0,-5)
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