Question Number 210298 by Spillover last updated on 05/Aug/24
![For the given system of simultaneous linear equation 2x_1 −2x_2 +3x_3 +4x_4 −x_5 =0 −x_3 −2x_4 +3x_5 =0 −x_1 +x_2 +2x_3 +5x_4 +2x_5 =0 x_1 −x_2 +2x_3 +3x_4 =0 (a)Write the augmented matrix and convert it into echelon form (b)Hence find all the solution](https://www.tinkutara.com/question/Q210298.png)
$${For}\:{the}\:{given}\:{system}\:{of}\:{simultaneous}\: \\ $$$${linear}\:{equation} \\ $$$$\mathrm{2}{x}_{\mathrm{1}} −\mathrm{2}{x}_{\mathrm{2}} +\mathrm{3}{x}_{\mathrm{3}} +\mathrm{4}{x}_{\mathrm{4}} −{x}_{\mathrm{5}} =\mathrm{0} \\ $$$$−{x}_{\mathrm{3}} −\mathrm{2}{x}_{\mathrm{4}} +\mathrm{3}{x}_{\mathrm{5}} =\mathrm{0} \\ $$$$−{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{3}} +\mathrm{5}{x}_{\mathrm{4}} +\mathrm{2}{x}_{\mathrm{5}} =\mathrm{0} \\ $$$${x}_{\mathrm{1}} −{x}_{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{3}} +\mathrm{3}{x}_{\mathrm{4}} =\mathrm{0} \\ $$$$\left({a}\right){Write}\:{the}\:{augmented}\:\:{matrix}\:{and}\:{convert} \\ $$$${it}\:{into}\:{echelon}\:{form} \\ $$$$\left({b}\right){Hence}\:{find}\:{all}\:{the}\:{solution} \\ $$$$ \\ $$