Q51 / 124 · NTA Abhyas (JEE Main) 2020 · Mathematics · Determinants

The following system of equations $5 x - 7 y + 3 z = 3, 5 x + y + 3 z = 7$ and $5 x + 3 y + 2 z = 5$ is

Solution

∆ = |\begin{matrix} 5 & - 7 & 3 \\ 5 & 1 & 3 \\ 5 & 3 & 2 \end{matrix}| = 5 (- 7) + 7 (- 5) + 3 (10)

= - 40 \neq 0

Hence, system of equation has non trivial unique solution as

(0, 0, 0)

does not satisfy system of equation.

Hence, the correct answer is option: 'B'.