The system of equations $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+\mathrm{a} z=12$ has no solution when $a=$

The system of equations $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+\mathrm{a} z=12$ has no solution when $a=$
  1. 5
  2. 6
  3. 7
  4. 8

Solution

$\because$ For no solution $\left|\begin{array}{lll}1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 5 & a\end{array}\right|=0 \Rightarrow 1(3 a-25)-2(a-10)+3(5-6)=0$ $\Rightarrow a=8$.

Asked in: AP EAMCET 2024 (19 May Shift 2)

Practice more Determinants questions on Aicharya