Question

Investigate for what values of $\lambda$, $\mu$ the simultaneous equations. $x+y+z=6,x+2y+3z=10,x+2y+\lambda z=\mu$ have a unique solution.

Answer 1

$A=\left[\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 2& \lambda \end{array}\right]$

for unique solution, $\left|A\right|=0$

for $\left|A\right|=0\Rightarrow \lambda =3$