Solve following system of homogeneous linear equations: `2x+3y+4z=0,\ \ x+y+z=0,\ \ 2x+5y-2z=0`

Explanation

We have given: `2x+3y+4z=0,\ \ x+y+z=0,\ \ 2x+5y-2z=0`

As we know that the system of linear equation can be written in matrix form as `AX = B`

`implies A=|(2,3,4),(1,1,1),(2,5,-2)|`,`X=[(x),(y),(z)]`,`B=[(0),(0),(0)]`

Now find the determinant of `A`,
`|A|= |(2,3,4),(1,1,1),(2,5,-2)|`

`|A|=2(1 xx (– 2) – 1 xx 5) – 3(1 xx (– 2) – 2 xx 1) + 4(1 xx 5 – 2 xx 1)`

`|A|=2(– 2 – 5) – 3(– 2 – 2) + 4(5 – 2)`

`|A|=17`

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