Задача 78008 Крамер X+2y+4z=31 5x+y+2z=29 3x-y+z=10...

6648c2ce387074050630cce5

5/18/2024 3:14:34 PM

Крамер
X+2y+4z=31
5x+y+2z=29
3x-y+z=10

5f3eaa23faf909182968dde0

7/31/2024 5:44:08 PM

★

Δ=
|1 2 4|
|5 1 2|=1-20+12-12+2-10=-27
|3 -1 1|

Δ_(x)=
|31 2 4|
|29 1 2| =31-116+40-40+62-58=-81
|10 -1 1|

Δ_(y)=
|1 31 4|
|5 29 2| =29+200+186-348-20-155=-108
|3 10 1|

Δ_(z)=
|1 2 31|
|5 1 29| = 10-155+174-93+29-100=-135
|3 -1 10|

x=( Δ_(x))/ Δ=(-81)/(-27)=3,
y=( Δ_(y))/ Δ=(-108_/(-27)=4,
z=( Δ_(z))/ Δ=(-135_/(-27)=5.

Ответ: (3; 4; 5).