# Solve each of the following systems of homogeneous linear equations : 2x + 3y + 4z = 0  x + y + z = 0  2x + 5y – 2z = 0

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Solve each of the following systems of homogeneous linear equations :

2x + 3y + 4z = 0

x + y + z = 0

2x + 5y – 2z = 0

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Given Equations :

2x + 3y + 4z = 0

x + y + z = 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,

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

= 2(– 2 – 5) – 3(– 2 – 2) + 4(5 – 2)

= 1×(– 7) – 3 × (– 4) + 4×3

= – 7 + 12 + 12

= 17

Since D ≠ 0,

So the system of equation has infinite solution.

Therefore,

The system of equation has only solution as

x = y = z = 0.