For the system of equations:

x + 2y + 3z = 1

2x + y + 3z = 2

5x + 5y + 9z = 4

The matrix equation corresponding to the above system is

Let A =

|A| = = 1(9-8) -2(18-15) +3(10-5) = 1-6+15 = 10

i.e., |A| 0

Hence, a unique solution exists of the above system.