Given as x + y – 2z = 0
2x + y – 3z =0
5x + 4y – 9z = 0
The system of any equation can be written in matrix form as AX = B
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
Here D = 0, therefore the system of equation has infinite solution.
Let z = k
⇒ x + y = 2k
And 2x + y = 3k
On using the Cramer’s rule
x = k
For D2/D
y = k
Hence x = y = z