If the system of equations λ$$x+(b$$−$$a)y+(c$$−$$a)z=0$$, $$(a$$−$$b)x+$$λ$$y+(c$$−$$b)z=0$$ and $$(a$$−$$c)x+(b$$−$$c)y+$$λ$$x=0$$ has a $$non-trivial$$ solutions, then the value of λ is

Question

If  the system of equations λ$$x+(b$$−$$a)y+(c$$−$$a)z=0$$,      $$(a$$−$$b)x+$$λ$$y+(c$$−$$b)z=0$$      and $$(a$$−$$c)x+(b$$−$$c)y+$$λ$$x=0$$      has a $$non-trivial$$  solutions, then the value of λ      is

Infinity Learn · Accepted Answer

As  the given system of equations has $$non-trivial$$  ⇒        |λ              b−a         c−aa−b          λ             c−ba−c       b−c            λ|$$=0$$     Whenλ$$=0$$,      then determinant  becomes $$skew-symmetric$$ determinants of odd order, which is equal to zero.  Thus, λ$$=0$$.

If the system of equations $λ x + (b - a) y + (c - a) z = 0,$ $(a - b) x + λ y + (c - b) z = 0$ and $(a - c) x + (b - c) y + λ x = 0$ has a non-trivial solutions, then the value of $λ$ is

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If the system of equations λx+(b−a)y+(c−a)z=0, (a−b)x+λy+(c−b)z=0 and (a−c)x+(b−c)y+λx=0 has a non-trivial solutions, then the value of λ is

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If the system of equations $λ x + (b - a) y + (c - a) z = 0,$ $(a - b) x + λ y + (c - b) z = 0$ and $(a - c) x + (b - c) y + λ x = 0$ has a non-trivial solutions, then the value of $λ$ is