# Gaussian Method

• Mar 18th 2014, 04:43 AM
haftakhan
Gaussian Method
I want to know the row operations to solve this question.

2 x-7y+4 z=9

x+9y-6z=1

-3x+8y+5z=1

First row operation i used is 2*R2-R1 then i used 3*R2+R3 but now i m dont know what to do to.
• Mar 18th 2014, 05:19 AM
romsek
Re: Gaussian Method
Quote:

Originally Posted by haftakhan
I want to know the row operations to solve this question.

2 x-7y+4 z=9

x+9y-6z=1

-3x+8y+5z=1

First row operation i used is 2*R2-R1 then i used 3*R2+R3 but now i m dont know what to do to.

first let's write this as an augmented matrix

$\begin{array}{cccc} 2x &-7y &+4z &=9 \\ x &+9y &-6z &=1 \\ -3x &+8y &+5z &=1 \end{array} \Rightarrow$

$\left( \begin{array}{ccccc} 2 &-7 &4 &|&9 \\ 1 &9 &-6 &|&1 \\ -3 &8 &5 &|&1 \end{array}\right)$

swap R1, R2

$\left( \begin{array}{ccccc} 1 &9 &-6 &|&1 \\ 2 &-7 &4 &|&9 \\ -3 &8 &5 &|&1 \end{array}\right)$

R2 --> R2 - 2R1

$\left( \begin{array}{ccccc} 1 &9 &-6 &|&1 \\ 0 &-25 &16 &|&7 \\ -3 &8 &5 &|&1 \end{array}\right)$

R3 --> R3 + 3R1

$\left( \begin{array}{ccccc} 1 &9 &-6 &|&1 \\ 0 &-25 &16 &|&7 \\ 0 &35 &-13 &|&4 \end{array}\right)$

R3 --> 5R3 + 7R2

$\left( \begin{array}{ccccc} 1 &9 &-6 &|&1 \\ 0 &-25 &16 &|&7 \\ 0 &0 &47 &|&69 \end{array}\right)$

R2 --> R2/(-25)

$\left( \begin{array}{ccccc} 1 &9 &-6 &|&1 \\ 0 &1 &-16/25 &|&-7/25 \\ 0 &0 &47 &|&69 \end{array}\right)$

R3 --> R3/47

$\left( \begin{array}{ccccc} 1 &9 &-6 &|&1 \\ 0 &1 &-16/25 &|&-7/25 \\ 0 &0 &1 &|&69/47 \end{array}\right)$

you can either solve it from here using back substitution or continue to reduce it.
• Mar 18th 2014, 07:21 AM
haftakhan
Re: Gaussian Method
x=182/47
y=31/47
z=69/47