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Question 94554: Matrices-and-determiminant/94544 (2007-08-26 21:09:08): I promise this is the last time I will beg for your help PLEASE HELP =I will pay you thru pay pal if I can get this answered in the next 1/2 hr. I am willing to pay PLEASE I AM DESPERate
Solve the system of equations by the Gaussian elimination method:
1. Solve the system of equations by the Gaussian elimination method:
2x+y-3z=1
3x-y+4z=6
x+2y-z=9
2. Solve the system of equations by the Gaussian elimination method:
x-y+z=17
x+y-z=-11
x-y-z=9
Again thank you in advance for your help.
0 solutions
Answer by chitra(359)  (Show Source):
You can put this solution on YOUR website! Alright here goes the solution for your question on solving equations by the method of gaussian elimination
2x + y - 3z = 1
3x - y + 4z = 6
x + 2y - z = 9
The given system can be written in the augmented form as:
[2 1 -3 : 1]
[3 -1 4 : 6]
[1 2 -1 : 9]
The operations performed are:
We shall first interchange the first row with the third row.
[1 2 -1 : 9]
[3 -1 4 : 6]
[2 1 -3 : 1]
Next: R2 - 3R1 and R3 - 2R1 are the operations which follow
[1 2 -1 : 9]
[0 -7 7 : -21]
[0 -3 -1 : -17]
R3 - R2 is the next opeartion.
[1 2 -1 : 9]
[0 -7 7 : -21]
[0 4 -8 : 4]
Lets divide R2/7 and R3/4
[1 2 -1 : 9]
[0 -1 1 : -3]
[0 1 -2 : 1]
Now R3 + R2 gives us the final step
[1 2 -1 : 9]
[0 -1 1 : -3]
[0 0 -1 : -2]
From this the given system of equations reduces to:
x + 2y - z = 9
-y + z = -3
-z = - 2
Hence, the value of z can be directly found out.
==> z = 2
now apply back substituion.
-y + z = -3
-y + 2 = -3
-y = -3 - 2
-y = -5
==> y = 5
Using y and z in the first equation we find the value of x.
x + 2y - z = 9
x + 10 - 2 = 9
x = 9 - 8
x = 1
Hence, the solution.
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Now the second question.
The given set of equations are:
x - y + z = 17
x + y - z = -11
x - y - z = 9
This in the augmented form can be written as:
[1 -1 1 : 17]
[1 1 -1 : -11]
[1 -1 -1 : 9]
Lets perform the firts row operation that is R2 - R1 and R3- R1
[1 -1 1 : 17]
[0 2 -2 : -28]
[0 0 -2 : -8]
Now we divide R2/2 and R3/2
[1 -1 1 : 17]
[0 1 -1 : -14]
[0 0 -1 : -4]
Thus the above augmented matrix can be written as:
x - y + z = 17
y - z = -14
-z = -4
This implies z = 4
By back substitution, we find the values of y and x.
y - 4 = -14
y = -14 + 4
==> y = -10
Now we find the value of x.
x - y + z = 17
x + 10 + 4 = 17
x + 14 = 17
x = 17 - 14
x = 3
Hence, the solution.
I hope all the stpes are quite clear..
You can get back to me for an online help in math at any time of yours.
Regards
Chitra
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