Solve gauss elimination method x+y+z=3,2x+3y+z=6,x-y-z=-3
Answers
Answer:
Step-by-step explanation:
Problem: Gauss Elimination x+y+z=3,2x+3y+z=6,x-y-z=-3 [ Calculator, Method and examples ]
Solution:
Your problem → Gauss Elimination x+y+z=3,2x+3y+z=6,x-y-z=-3
Total Equations are 3
x+y+z=3→(1)
2x+3y+z=6→(2)
x-y-z=-3→(3)
Converting given equations into matrix form
1 1 1 3
2 3 1 6
1 -1 -1 -3
R2←R2-2×R1
=
1 1 1 3
0 1 -1 0
1 -1 -1 -3
R3←R3-R1
=
1 1 1 3
0 1 -1 0
0 -2 -2 -6
R1←R1-R2
=
1 0 2 3
0 1 -1 0
0 -2 -2 -6
R3←R3+2×R2
=
1 0 2 3
0 1 -1 0
0 0 -4 -6
R3←R3÷-4
=
1 0 2 3
0 1 -1 0
0 0 1 1.5
R1←R1-2×R3
=
1 0 0 0
0 1 -1 0
0 0 1 1.5
R2←R2+R3
=
1 0 0 0
0 1 0 1.5
0 0 1 1.5
i.e.
x=0
y=1.5
z=1.5
Solution By Gauss jordan elimination method
x=0,y=1.5andz=1.5
AtoZmath2
00:00/00:00
Solution provided by AtoZmath.com
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Problem: Gauss Elimination x+y+z=3,2x+3y+z=6,x-y-z=-3 [ Calculator, Method and examples ]
Slution:
Your problem → Gauss Elimination x+y+z=3,2x+3y+z=6,x-y-z=-3
Total Equations are 3
x+y+z=3→(1)
2x+3y+z=6→(2)
x-y-z=-3→(3)
Converting given equations into matrix form
1 1 1 3
2 3 1 6
1 -1 -1 -3
R2←R2-2×R1
=
1 1 1 3
0 1 -1 0
1 -1 -1 -3
R3←R3-R1
=
1 1 1 3
0 1 -1 0
0 -2 -2 -6
R1←R1-R2
=
1 0 2 3
0 1 -1 0
0 -2 -2 -6
R3←R3+2×R2
=
1 0 2 3
0 1 -1 0
0 0 -4 -6
R3←R3÷-4
=
1 0 2 3
0 1 -1 0
0 0 1 1.5
R1←R1-2×R3
=
1 0 0 0
0 1 -1 0
0 0 1 1.5
R2←R2+R3
=
1 0 0 0
0 1 0 1.5
0 0 1 1.5
i.e.
x=0
y=1.5
z=1.5
Solution By Gauss jordan elimination method
x=0,y=1.5andz=1.5
AtoZmath2
00:00/00:00
Solution provided by AtoZmath.com
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