Q116 / 170 · Manipal (MET) 2021 · Mathematics
The system of linear equations $x+y+z=0$, $2 x+y-z=0,3 x+2 y=0$ has
- Ano solution
- Ba unique solution
- Correct answerCinfinitely many solutions
- DNone of these
Solution
Given system of equations are
$x+y+z=0,2 x+y-z=0,3 x+2 y=0$
Let $\Delta=\left|\begin{array}{rrr}1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & 0\end{array}\right|=1(0+2)-1(0+3)+1(4-3)$ $=+2-3+1=0$
Hence, it has infinitely many solutions.
Let $\Delta=\left|\begin{array}{rrr}1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & 0\end{array}\right|=1(0+2)-1(0+3)+1(4-3)$ $=+2-3+1=0$
Hence, it has infinitely many solutions.
Hence, the correct answer is option: 'C'.