x + y + z = 0$\quad$$\quad$$\quad$$\quad$...(1)
2x + 3y + z = 0$\quad$$\quad$$\quad$$\quad$ ...(2)
x + 2y = 0 $\quad$$\quad$$\quad$$\quad$ ... (3)
From equation (3), we have
x = - 2y
Putting this value of x in equations (1), we
get$\quad$$\quad$ - 2y + y + z = 0 $\Rightarrow $ y = z
Hence x = - 2z
Thus, the solution of the given system of equations is (-2z, z, z), where z is a parameter (Z $\in$ R). Hence the system has infinite number of solutions including zero solution.