Решите методом Гаусса систему уравнений: а) x+y+z=1 б) -2x+7y-4z=1 x-y-z=...

Orlova2000 @Orlova2000

July 2022 1 1 Report

Решите методом Гаусса систему уравнений:
а) x+y+z=1 б)     -2x+7y-4z=1
   x-y-z=1 4x-8y+5x=1
-x+y+z=-1        3x+2y-4z=1

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555888999

$\left \{ {{x+y+z=1} \atop {x-y-z=1}} \atop {-x+y+z=-1}} \right. \\ 
 \left \{ {{x+y+z=1} \atop {2x=2}} \atop {2y+2z=0}} \right. \\ 
 \left \{ {{x+y+z=1} \atop {x=1}} \atop {y=-z}} \right. \\ 
 \left \{ {{x=1} \atop {y}} \atop {-y}} \right.$

где у любое число

$\left \{ {{-2x+7y-4z=1}|*-1 \atop {4x-8y+5z=1}} \atop {3x+2y-4z=1} \right. \\ 
 \left \{ {{2x-7y+4z=-1} \atop {4x-8y+5z=1}} \atop {3x+2y-4z=1}} \right. \\ 
 \left \{ {{2x-7y+4z=-1} |*-5\atop {4x-8y+5z=1}}|*4 \atop {5x-5y=0}} \right. \\ 
 \left \{ {{-10x+35y-20z=5} \atop {16x-32y+20z=4}} \atop {5x-5y=0}} \right. \\ 
 \left \{ {{-10x+35y-20z=5} \atop {6x+3y=9}}|*5 \atop {5x-5y=0}}|*3 \right. \\ 
 \left \{ {{-2x+7y-4z=1} \atop {30x+15y=45}} \atop {45x=45}} \right. \\ 
 x=1,y=1,z=1$

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