Question 903022: 2a + 3b + c + 2d = 20
4a + b + 2c + 5d = 50
a + 2b + 3c + d = 10
2a + 4b + 2c + 3d = 15
Found 3 solutions by Fombitz, richwmiller, sonic1:
Answer by Fombitz(32388)   (Show Source):
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! gauss jordan
2,3,1,2,20
4,1,2,5,50
1,2,3,1,10
2,4,2,3,15
divide row 1 by 2
1,3/2,1/2,1,10
4,1,2,5,50
1,2,3,1,10
2,4,2,3,15
add down (-4) *row 1 to row 2
1,3/2,1/2,1,10
0,-5,0,1,10
1,2,3,1,10
2,4,2,3,15
add down (-1) *row 1 to row 3
1,3/2,1/2,1,10
0,-5,0,1,10
0,1/2,5/2,0,0
2,4,2,3,15
add down (-2) *row 1 to row 4
1,3/2,1/2,1,10
0,-5,0,1,10
0,1/2,5/2,0,0
0,1,1,1,-5
divide row 2 by -5
1,3/2,1/2,1,10
0,1,0,1/-5,-2
0,1/2,5/2,0,0
0,1,1,1,-5
add down (-1/2) *row 2 to row 3
1,3/2,1/2,1,10
0,1,0,1/-5,-2
0,0,10/4,-1/-10,1
0,1,1,1,-5
add down (-1) *row 2 to row 4
1,3/2,1/2,1,10
0,1,0,1/-5,-2
0,0,5/2,1/10,1
0,0,1,-6/-5,-3
divide row 3 by 5/2
1,3/2,1/2,1,10
0,1,0,1/-5,-2
0,0,1,2/50,2/5
0,0,1,6/5,-3
add down (-1) *row 3 to row 4
1,3/2,1/2,1,10
0,1,0,1/-5,-2
0,0,1,1/25,2/5
0,0,0,145/125,-17/5
divide row 4 by 29/25
1,3/2,1/2,1,10
0,1,0,1/-5,-2
0,0,1,1/25,2/5
0,0,0,1,-425/145
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-1/25) *row 4 to row 3
1,3/2,1/2,1,10
0,1,0,1/-5,-2
0,0,1,0,1875/3625
0,0,0,1,-85/29
add up (-1/-5) *row 4 to row 2
1,3/2,1/2,1,10
0,1,0,0,375/-145
0,0,1,0,15/29
0,0,0,1,-85/29
add up (-1) *row 4 to row 1
1,3/2,1/2,0,375/29
0,1,0,0,75/-29
0,0,1,0,15/29
0,0,0,1,-85/29
add up (0) *row 3 to row 2
1,3/2,1/2,0,375/29
0,1,0,0,2175/-841
0,0,1,0,15/29
0,0,0,1,-85/29
add up (-1/2) *row 3 to row 1
1,6/4,0,0,21315/1682
0,1,0,0,75/-29
0,0,1,0,15/29
0,0,0,1,-85/29
add up (-3/2) *row 2 to row 1
1,0,0,0,-55680/-3364
0,1,0,0,75/-29
0,0,1,0,15/29
0,0,0,1,-85/29
final
1,0,0,0,480/29
0,1,0,0,75/-29
0,0,1,0,15/29
0,0,0,1,-85/29
1,0,0,0,480/29 = 16.5517241
0,1,0,0,75/-29 = -2.5862069
0,0,1,0,15/29 = 0.51724138
0,0,0,1,-85/29 = -2.93103448
"480/29","75/-29","15/29","-85/29"
(480/29,75/-29,15/29,-85/29)
using determinants
Summary
determinant = -29
a = -480/-29 = 480/29 = 16.5517241
b = 75/-29 = 75/-29 = -2.5862069
c = -15/-29 = 15/29 = 0.51724138
d = 85/-29 = 85/-29 = -2.93103448
Answer by sonic1(3)  (Show Source):
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