gauss elimination method for x+2y-3z=9,2x-y+z=0,4x-y+z=4
Answers
Answer:
(x,y,z)=(2,0,-4)
First we create the extended matrix from the equations
Using the elementary operations
Substract to the 2nd line the first one, and the 3rd one twice the first:
Divide the first line by 2, the 2nd one by -5 and substract to the 3rd the 2nd:
Divide the 3rd by 4:
Add the 3rd to the 2nd:
Substract the 2nd to the 1st
Add the 3rd multiplied by 3/2:
The answer is determined:
x=2
y=0
z=-4
You can check they are correct, by entering in the original formulas.
Step-by-step explanation:
Hope this helps:) ジョセフ
Answer:
4.4286 + 2(2.8571) - 3(1.5429) = 18
4.4286 + 5.7142 - 4.6286 = 18
9.1428 = 18
This equation is not valid, therefore, there is no solution to the system of equations.
Step-by-step explanation:
From the above question,
They have given :
Gauss elimination method:
Step 1:
x + 2y - 3z = 9
2x - y + z = 0
4x - y + z = 4
Step 2:
Multiply the first equation by 2.
2x + 4y - 6z = 18
2x - y + z = 0
4x - y + z = 4
Step 3:
Add the first and third equations.
2x + 4y - 6z = 18
2x - y + z = 0
6x + 3y - 5z = 22
Step 4:
Multiply the second equation by -3.
2x + 4y - 6z = 18
-6x + 3y - 3z = 0
6x + 3y - 5z = 22
Step 5:
Add the second and third equations.
2x + 4y - 6z = 18
-6x + 3y - 3z = 0
0 + 7y - 8z = 40
Step 6:
Divide the third equation by 7.
2x + 4y - 6z = 18
-6x + 3y - 3z = 0
y - 2z = 5.714
Step 7:
Substitute y - 2z = 5.714 in the second equation.
2x + 4y - 6z = 18
-6x + 3(5.714) - 3z = 0
-6x + 17.142 - 3z = 0
Step 8:
Divide the second equation by -6.
2x + 4y - 6z = 18
x - 2.8571z = 0
y - 2z = 5.714
Step 9:
Substitute x - 2.8571z = 0 in the first equation.
2(2.8571z) + 4y - 6z = 18
5.7142z + 4y - 6z = 18
y = 2.8571
Step 10:
Substitute y = 2.8571 in the third equation.
2.8571 - 2z = 5.714
2z = 3.0857
z = 1.5429
Step 11:
Substitute z = 1.5429 in the second equation.
x - 2.8571(1.5429) = 0
x = 4.4286
Step 12:
Substitute x = 4.4286 and z = 1.5429 in the first equation.
4.4286 + 2(2.8571) - 3(1.5429) = 18
4.4286 + 5.7142 - 4.6286 = 18
9.1428 = 18
This equation is not valid, therefore, there is no solution to the system of equations.
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