SOLUTION: 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

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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