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

Explanation

We have given :the system of homogeneous equations:`x+y+z=0``x-2y+z=0`
`3x+6y-5z=0`

It can be written in matrix form as

`A=[(1,1,-1),(1,-2,1),(3,6,-5)]`

Now apply `R_2->R_2-R_1`and `R_3->R_3-3R_1`

`A=[(1,1,-1),(0,-3,2),(0,3,-2)]`

`|A|=0` and rank of `A=2`, submatrix is `[(1,1),(0,-3)]`

Hence we get

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