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

Question

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

System is inconsistent if $\lambda=1$ and $\mu \neq 13$

System has unique solution if $\lambda \neq 1$ and $\mu \neq 13$

System has infinite number of solutions if $\lambda=1$ and $\mu=13$

Solution

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