Solve the following system of homogeneous equations: `x+y-z=0` `x-2y+z=0` `3x+6y-5z=0`

Explanation

Given system of equation is,
`x+y-z=0`


`x-2y+z=0`


`3x+6y-5z=0`
Arranging the above equations in form of matrix and finding the coefficient of matrix, we get,
`A=[(1,1,-1),(1,-2,1),(3,6,-5)]`
`R_2->R_2-R_1`
`R_3->R_3-3R_1`
`A∼[(1,1,-1),(0,-3,2),(0,3,-2)]`
`det(A)=0` as 2nd and 3rd rows are identical.
as, ρ(A)=2, submatrix is,
`[(1,1),(0,-3)]`
we get,


`x+y−z=0`


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