Gauss-Jordan Method

[ocgirl83]

Use the Gauss-Jordan method to solve each system of equations. For systems in three variables with infinitely many solutions, give the solution with a z arbitrary; for any such equations with four variables, let w be the arbitrary variable.

I have three of these problems and do not understand how to begin with them. if anyone can offer some assistance it would be greatly appreciated.

16. x+ 2y =5
2x +y =-2

18. 2x- 3y = 10
2x +2y = 5

20. 2x - 5y - 10 = 0
3x + y - 15 = 0

 

[ocgirl83]

any help is appreciated. Just how to set up the problems.

I know that you have to get it into a matrix and put in 0,1,k, j..beyond that im clueless.

 

[galactus]

I will step through #1 for you. You try #2 and #3. If you get hung up, write back.

#3 has more vaiables than equations, so that ought to tell you something.

\(\displaystyle \left[\begin{array}{cc}1&2&5\\\2&1&-2\end{array}\right]\)

\(\displaystyle \(-2)R_{1}+R_{2}\)-->\(\displaystyle R_{2}:\)

\(\displaystyle \left[\begin{array}{cc}1&2&5\\\0&-3&-12\end{array}\right]\)

\(\displaystyle \frac{-1}{3}R_{2}\)-->\(\displaystyle R_{2}:\)

\(\displaystyle \left[\begin{array}{cc}1&2&5\\\0&1&4\end{array}\right]\)

\(\displaystyle \(-2)R_{2}+R_{1}\)-->\(\displaystyle R_{1}:\)

\(\displaystyle \left[\begin{array}{cc}1&0&-3\\\0&1&4\end{array}\right]\)

There, \(\displaystyle x=-3\) and \(\displaystyle y=4\)

As you can see, the idea is to reduce it down until you get diagonal ones...if possible. Your text and teacher should be around for the basics behind Gaussian elimination.

Hope this helps.

 

[ocgirl83]

thank you.