Question

Solve using matrices,
matrices, the system
2x - 3y +z = 14
4x + 4y -3z = 6
3x+2y -3z=-2​

Answer 1

Resposta:

S= {(136/25; 32/25; 174/25)}

I) 2x - 3y + z = 14

II) 4x + 4y - 3z = 6

III) 3x + 2y - 3z = - 2

Elimination method

I) 2x - 3y + z = 14 .(3)

6x - 9y + 3z = 42

adding equation I and II

I) 6x - 9y + 3z = 42

II) 4x + 4y - 3z = 6

10x - 5y = 48

Elimination method

II) 3x + 2y - 3z = - 2 .(-1)

- 3x - 2y + 3z = 2

adding equation III and II

III) - 3x - 2y + 3z = 2

II) 4x + 4y - 3z = 6

x + 2y = 8

System:

I) 10x - 5y = 48

II) x + 2y = 8

Elimination method

II) x + 2y = 8 .(-10)

-10x - 20y = - 80

adding equation I and II

I) 10x - 5y = 48

II) -10x - 20y = - 80

- 25y = - 32 .(-1)

y = 32/25

Substituting y in equation II

II) x + 2y = 8

x + 2. 32/25 = 8

x + 64/25 = 8

x = 8 - 64/25

x = 200/25 - 64/25

x = 136/25

Substituting x and y in equation I

I) 2x - 3y + z = 14

2.136/25 - 3.32/25 + z = 14

272/25 - 96/25 + z = 14

176/25 + z = 14

z = 14 - 176/25

z = 350/25 - 176/25

z = 174/25

( x , y , z ) = ( 136/25 , 32/25 , 174/25 )