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Solve the Following System of Linear Equation Using Matrix Method: - Mathematics

Sum

Solve the following system of linear equation using matrix method: 
`1/x + 1/y +1/z = 9`

`2/x + 5/y+7/z = 52`

`2/x+1/y-1/z=0`

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Solution

`Let  1/x=X; 1/y=Y;1/Z= Z`
X+Y+Z = 9            ....(1)
`2X+5Y+7Z=52`     ....(2)
`2X+Y-Z =0 `         .....(3)
AX = B
`[(1, 1, 1),(2,5,7),(2,1,-1)][(X),(Y),(Z)]=[(9),(52),(0)]`
`R_2 rArr R_2- R_1 and R_3 rArr R_3 - 2R_1`
`[(1, 1, 1),(0,3,5),(0,-1,-3)][(X),(Y),(Z)]=[(9),(34),(-18)]`

`R_2rArr R_2+.3R_3`
`[(1, 1, 1),(0,0,-4),(0,-1,-3)][(X),(Y),(Z)]=[(9),(-20),(-18)]`

`[(X+Y+Z),(-4Z),(-Y -3Z)]_(3xx1) =[(9),(-20),(-18)]_(3xx1)`

∴ -4Z =-20 ⇒ Z=5
∴ -Y- 3Z = -18

∴ Y + 3Z= -18
∴Y + 15 = 18 
∴ Y = 3
∴ X+Y+Z =9
∴ X + 3+ 5+9 

X=1

∴ `1/X = x rArr 1/1= x`        ∴ x=1

`1/Y = 3`      ∴ `1/3 = y`
`1/Z = z`      ∴ `z=1/5`

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