Given Equations :
x + y – 2z = 0
2x + y – 3z = 0
5x + 4y – 9z = 0
Any system of equation can be written in matrix form as AX = B
Now finding the Determinant of these set of equations,
= 1(1×(– 9) – 4×(– 3)) – 1(2×(– 9) – 5×(– 3)) – 2(4×2 – 5×1)
= 1(– 9 + 12) – 1(– 18 + 15) – 2(8 – 5)
= 1×3 –1 × (– 3) – 2×3 = 3 + 3 – 6 = 0
Since,
D = 0
so the system of equation has infinite solution.
Now,
let z = k
⇒ x + y = 2k
And,
2x + y = 3k
Now,
using the cramer’s rule
Hence,
x = y = z = k.