Consider the system of linear equations $x+y+z=4 \mu, x+2 y+2 \lambda z=10 \mu, x+3 y+4 \lambda^2 z=\mu^2+15$ where $\lambda, \mu \in \mathbf{R}$. Which one of the following statements is NOT correct ?

Question

The system has unique solution if $\lambda \neq \frac{1}{2}$ and $\mu \neq 1,15$

The system has infinite number of solutions if $\lambda=\frac{1}{2}$ and $\mu=15$

The system is consistent if $\lambda \neq \frac{1}{2}$

The system is inconsistent if $\lambda=\frac{1}{2}$ and $\mu \neq 1$

Solution

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