Question -
Answer -
Given
2x + 3y + 4z = 0
x + y + z = 0
2x + 5y – 2z = 0
Any system of equationcan be written in matrix form as AX = B
Now finding theDeterminant 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 thesystem of equation has infinite solution.
Therefore the systemof equation has only solution as x = y = z = 0.