Question

If the system of linear equations $(1+\alpha )x+\beta y+z=2,\alpha x+(1+\beta )y+z=3,\alpha x+\beta y+2z=2$ has unique solution then the ordered pair $(\alpha ,\beta )$ will be

• A. (1, –3)
• B. (–3, 1)
• C. (2, 4)
• D. (–4, 2)

Answer 1

The correct option is C (2, 4)

For unique solution $=\left|\begin{array}{ccc}1+\alpha & \beta & 1\\ \alpha & 1+\beta & 1\\ \alpha & \beta & 2\end{array}\right|\ne 0$
$R_1\to R_1-R_2$
$R_2\to R_2-R_3\left|\begin{array}{ccc}1& -1& 0\\ 0& 1& -1\\ \alpha & \beta & 2\end{array}\right|\ne 0\Rightarrow \alpha +\beta \ne -2$