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Question Number 161429 by greg_ed last updated on 17/Dec/21

$$\mathrm{help}\mathrm{me}!$$$$\{\begin{array}{l}x+3y+z=2\\ -3x+4y+2z=3\\ -2x+7y+3z=5\end{array}$$$$\mathbf{G}\mathrm{auss}\mathrm{Method}...$$

Commented by 1549442205PVT last updated on 18/Dec/21

$$thegivensystemofequationsisnot$$$$compatiblebecause$$$$△=\left|\begin{array}{c}131\\ -342\\ -273\end{array}\right|=12-12-21+8+27-14=0$$$$thesystemisequivalentto$$$$\{\begin{array}{l}x+3y+z=2\\ 13y+5z=9\end{array}\Rightarrow \{\begin{array}{l}x=\frac{2z-1}{13}\\ y=\frac{9-5z}{13}\end{array}$$$$or\{\begin{array}{l}x=\frac{2t-1}{13}\\ y=\frac{9-5t}{13}\\ z=t\end{array}\mathrm{\forall }t\in R$$

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