Gauss-Jordan elimination
- Thread starter kayesal
- Start date
Hello, kayesal!
Exactly where is your difficulty?
\(\displaystyle \;\;\)You know nothing about the Elimination?
\(\displaystyle \;\;\)You don't know how to get the 1's and 0's ?
\(\displaystyle \;\;\)You make errors in arithmetic?
I can do these for you all day
\(\displaystyle \;\;\)but if no Learning is taking place, it's just a waste of time.
\(\displaystyle \begin{array}{cccc}:\\: \\ R_2-R_1 \\ R_3-5\cdot R_1\end{array}\,\begin{vmatrix}1 & -1 & 4 & | & 3 \\ 0 & 3 & -3 & | & 9 \\ 0 & 5 & -19 & | & -13\end{vmatrix}\)
\(\displaystyle \begin{array}{cccc}:\\:\\: \\ R_2\div3\end{array}\,\begin{vmatrix}1 & -1 & 4 & | & 3 \\0 & 1 & -1 & | & 3 \\ 0 & 5 & -19 & | &-13\end{vmatrix}\)
\(\displaystyle \begin{array}{ccccc}R_1+R_2 \\:\\:\\ R_3-5\cdot R_2\end{array}\,\begin{vmatrix}1 & 0 & 3 & | & 6 \\ 0 & 1 & -1 & | & 3 \\ 0 & 0 & -14 & | & -28\end{vmatrix}\)
\(\displaystyle \begin{array}{cccccc}:\\: \\:\\ R_3\div(-14)\end{array}\,\begin{vmatrix}1 & 0 & 3 & | & 6 \\ 0 & 1 & -1 & | & 3 \\ 0 & 0 & 1 & | & 2\end{vmatrix}\)
\(\displaystyle \begin{array}{ccccc}R_1-3\cdot R_3\\ R_2+R_3 \\:\\: \end{array}\,\begin{vmatrix}1 & 0 & 0 & | 0\\ 0 & 1 & 0 & | 5\\ 0 & 0 & 1 & | 2\end{vmatrix}\)
Solution: \(\displaystyle \,(x,\,y,\,z)\:=\
0,\,5,\,2)\)
Exactly where is your difficulty?
\(\displaystyle \;\;\)You know nothing about the Elimination?
\(\displaystyle \;\;\)You don't know how to get the 1's and 0's ?
\(\displaystyle \;\;\)You make errors in arithmetic?
I can do these for you all day
\(\displaystyle \;\;\)but if no Learning is taking place, it's just a waste of time.
We have: \(\displaystyle \:\begin{vmatrix}1 & -1 & 4 & | & 3 \\ 1 & 2 & 1 & | & 12 \\ 5 & 0 & 1 & | & 2\end{vmatrix}\)
\(\displaystyle \begin{array}{cccc}:\\: \\ R_2-R_1 \\ R_3-5\cdot R_1\end{array}\,\begin{vmatrix}1 & -1 & 4 & | & 3 \\ 0 & 3 & -3 & | & 9 \\ 0 & 5 & -19 & | & -13\end{vmatrix}\)
\(\displaystyle \begin{array}{cccc}:\\:\\: \\ R_2\div3\end{array}\,\begin{vmatrix}1 & -1 & 4 & | & 3 \\0 & 1 & -1 & | & 3 \\ 0 & 5 & -19 & | &-13\end{vmatrix}\)
\(\displaystyle \begin{array}{ccccc}R_1+R_2 \\:\\:\\ R_3-5\cdot R_2\end{array}\,\begin{vmatrix}1 & 0 & 3 & | & 6 \\ 0 & 1 & -1 & | & 3 \\ 0 & 0 & -14 & | & -28\end{vmatrix}\)
\(\displaystyle \begin{array}{cccccc}:\\: \\:\\ R_3\div(-14)\end{array}\,\begin{vmatrix}1 & 0 & 3 & | & 6 \\ 0 & 1 & -1 & | & 3 \\ 0 & 0 & 1 & | & 2\end{vmatrix}\)
\(\displaystyle \begin{array}{ccccc}R_1-3\cdot R_3\\ R_2+R_3 \\:\\: \end{array}\,\begin{vmatrix}1 & 0 & 0 & | 0\\ 0 & 1 & 0 & | 5\\ 0 & 0 & 1 & | 2\end{vmatrix}\)
Solution: \(\displaystyle \,(x,\,y,\,z)\:=\
0,\,5,\,2)\)I can set it up get the first and second 1's and 0's then I get messed up in the math. I had no where near the answer you had I had all kinds of fractionsand then I just get stuck. Thanks for the help though, I will look closely at your answer to figure out where I went wrong.
