Question

Solve the following equations by reduction method: 

x + y + z = 6,

3x - y + 3z = 10

5x + y - 4z = 3 

Answer 1

Given equation in matrix form as 

`[(1,1,1),(3,-1,3),(5,1,-4)] [(x),(y),(z)] = [(6),(10),(3)]`

R₂ → R₂ - 3 R₁ and R₃ → R₃ - 5 R₁

`[(1,1,1),(0,-4,0),(0,-4,-9)] [(x),(y),(z)] = [(6),(-8),(-27)]`

R₁ → R₃  - R₂ 

`[(1,1,1),(0,-4,0),(0,0,-9)] [(x),(y),(z)] = [(6),(-8),(-19)]`

∴ x + y + z = 6         .......(i)

∴ - 4y = - 8              ........(ii)

∴ - 9z = -19            .....(iii)

From (iii) , z = `19/9`

From (ii) , y = 2

From (i) , x + 2 + `19/9` = 6

`=> "x" + 37/9 = 6`

`=> "x" = 17/9`

∴ `"x" = 17/9 , "y" = 2 , "z" = 19/9`