Consider the system of linear equations $x+y+z=5,x+2y+{\lambda }^{2}z=9$ and $x+3y+\lambda z=\mu$, where $\lambda ,\mu \in R$. Then, which of the following statement is NOT correct ?

• A

  System has infinite number of solution if $\lambda =1$ and $\mu =13$
• B

  System is inconsistent if $\lambda =1$ and $\mu \ne 13$
• Correct answer
  C

  System has unique solution if $\lambda \ne 1$ and $\mu \ne 13$
• D

  System is consistent if $\lambda \ne 1$ and $\mu =13$

Hence, the correct answer is option: 'C'.