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

Explanation

Given Equations :` 3x + y + z = 0`

` x – 4y + 3z = 0`

` 2x + 5y – 2z = 0 `

Any system of equation can be written in matrix form as AX = B
Now finding the Determinant of these set of equations,

D=`abs([3,1,1],[1,-4,3],[2,5,-2])`

=`3(– 4×(– 2) – 3×5) – 1(1×(– 2) – 3×2) + 1(1×5 – 2×(– 4))`

= `3×(– 7) –1 × (– 8) + 1×13`

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