A matrix is given in echelon form This is my first time posting a question and I'm really stuck on this one.
Help would be appreciated. 
I'm given this matrix 
$$\left[
\begin{array}{ccc|c}
2&3&0&9\\0&1&\lambda+6&4\\
0&0&\lambda^2-5\lambda+6&9-3\lambda
\end{array}\right],
$$
and I need to find for which  λ ∈ ℝ this matrix has 


*

*one solution

*no solutions

*infinite solutions


see if there is a pivot in column three. you have one if $\lambda \neq 2$ and $\lambda \neq 3$ implying in these case you have a unique solution. now all you are left with are the cases $\lambda = 2$  and $\lambda = 3.$ i will let you handle those.
