We consider the system given by the following augmented matrix $$ \left[\begin{array}{rrr|r}1 & -2 & 1 & 4 \ 0 & 1 & -1 & 3 \ 0 & 0 & \alpha^{2}-\alpha-2 & \alpha+1\end{array} ight] $$ Determine the value (s) of $$ \alpha $$ for which the system has exactly one solution. $$ \alpha \in(-\infty, 2) \cup(2, \infty) $$ $$ \alpha \in(-\infty, 1) \cup(1, \infty) $$ $$ \alpha
eq-1 $$ $$ \alpha $$ is any real number None of the given options are correct

Question

We consider the system given by the following augmented matrix $$ \left[\begin{array}{rrr|r}1 & -2 & 1 & 4 \ 0 & 1 & -1 & 3 \ 0 & 0 & \alpha^{2}-\alpha-2 & \alpha+1\end{array}ight] $$ Determine the value (s) of $$ \alpha $$ for which the system has exactly one solution. $$ \alpha \in(-\infty, 2) \cup(2, \infty) $$ $$ \alpha \in(-\infty, 1) \cup(1, \infty) $$ $$ \alpha 
eq-1 $$ $$ \alpha $$ is any real number None of the given options are correct

Mann Ruiz · Accepted Answer

The system has exactly one solution for $$ \alpha $$ values except $$ \alpha = 2 $$ and $$ \alpha = -1 $$. None of the given options are correct.

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