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Question
Solve the following equations by reduction method:
x+ y+z = 6,
3x-y+3z = 10
5x+ y-4z = 3
Solution
Given equation in matrix form as
`[(1,1,1),(3,-1,3),(5,1,-4)] [(x),(y),(z)] = [(6),(10),(3)]`
R2 → R2 - 3 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`
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