Mathematics, 07.04.2020 15:48 haileysolis5
For problem (1) and (2), use Gauss-Jordan reduction to transform the augmented matrix of each system to RREF. Use it to discuss the solutions of the system (i. e., no solutions, a unique solution, or infinitely many solutions).(1)2x+ 3y+z= 2x+ 9y= 12x+y+ 3z= 5
Answers: 1
, 
and 
![\left[\begin{array}{ccc}2&3&1\\2&9&0\\12&1&3\end{array}\right|\left\begin{array}{c}5\\5\\5\end{array}\right]](/tpl/images/0586/3684/17aed.png)
)![\left[\begin{array}{ccc}2&3&1\\0&6&-1\\12&1&3\end{array}\right|\left\begin{array}{c}5\\0\\5\end{array}\right]](/tpl/images/0586/3684/f1123.png)
)![\left[\begin{array}{ccc}2&3&1\\0&6&-1\\0&-17&-3\end{array}\right|\left\begin{array}{c}5\\0\\-25\end{array}\right]](/tpl/images/0586/3684/a51f0.png)
)![\left[\begin{array}{ccc}1&\frac32&\frac12\\0&6&-1\\0&-17&-3\end{array}\right|\left\begin{array}{c}\frac52\\0\\-25\end{array}\right]](/tpl/images/0586/3684/039b3.png)
![\left[\begin{array}{ccc}1&\frac32&\frac12\\ \\0&1&\frac{-1}{6}\\ \\0&-17&-3\end{array}\right|\left\begin{array}{c}\frac52\\ \\0\\ \\-25\end{array}\right]](/tpl/images/0586/3684/60fc1.png)
from row 1 
![\left[\begin{array}{ccc}1&0&\frac34\\ \\0&1&\frac{-1}{6}\\ \\0&-17&-3\end{array}\right|\left\begin{array}{c}\frac52\\ \\0\\ \\-25\end{array}\right]](/tpl/images/0586/3684/4bc50.png)
![\left[\begin{array}{ccc}1&0&\frac34\\ \\0&1&-\frac{1}{6}\\ \\0&0&-\frac{35}{6}\end{array}\right|\left\begin{array}{c}\frac52\\ \\0\\ \\-25\end{array}\right]](/tpl/images/0586/3684/7fdbc.png)
![\left[\begin{array}{ccc}1&0&\frac34\\ \\0&1&-\frac{1}{6}\\ \\0&0&1\end{array}\right|\left\begin{array}{c}\frac52\\ \\0\\ \\\frac{30}7\end{array}\right]](/tpl/images/0586/3684/4e618.png)
from row 1 
![\left[\begin{array}{ccc}1&0&0\\ \\0&1&-\frac{1}{6}\\ \\0&0&1\end{array}\right|\left\begin{array}{c}-\frac57\\ \\0\\ \\\frac{30}7\end{array}\right]](/tpl/images/0586/3684/996a5.png)
to row 2 
![\left[\begin{array}{ccc}1&0&0\\ \\0&1&0\\ \\0&0&1\end{array}\right|\left\begin{array}{c}-\frac57\\ \\\frac57\\ \\\frac{30}7\end{array}\right]](/tpl/images/0586/3684/6672f.png)
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For problem (1) and (2), use Gauss-Jordan reduction to transform the augmented matrix of each system...
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