The value of λfor which the system of equations x−$$2y$$−$$2z=$$λx,$$x+2y+z=$$λy,−x−y−λ$$z=0$$ has a $$non-trivial$$ solution is

Question

The value of λfor which the system of equations x−$$2y$$−$$2z=$$λx,$$x+2y+z=$$λy,−x−y−λ$$z=0$$ has a $$non-trivial$$ solution is

Infinity Learn · Accepted Answer

The system has a non – trivial solution⇒Δ$$=0$$ ⇒$$1$$−λ−$$2$$−$$212$$−λ$$1$$−$$1$$−$$1$$−λ$$=0$$    apply $$R1$$→ $$R1+$$ $$R3$$, $$R2$$→ $$R2+$$ $$R3$$ ⇒−λ−$$3$$−$$2-$$λ$$01$$−λ$$1$$−λ−$$1$$−$$1$$−λ$$=0$$ ⇒λ−$$3$$−$$2-$$λ$$01$$−λ$$1$$−λ$$1$$−$$1$$−λ$$=0$$ ⇒λ−λ$$1$$−λ$$+11$$−λ$$-0+1-31$$−λ$$+1$$−λ$$2+$$λ$$=0$$ ⇒λλ$$-12-$$λ$$-12=0$$ ⇒λ$$-13=0$$ ⇒λ$$=1$$  ⇒λ$$=1$$

The value of $λ$ for which the system of equations $x - 2 y - 2 z = λ x, x + 2 y + z = λ y, - x - y - λ z = 0$ has a non-trivial solution is

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The value of λfor which the system of equations x−2y−2z=λx,x+2y+z=λy,−x−y−λz=0 has a non-trivial solution is

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The value of $λ$ for which the system of equations $x - 2 y - 2 z = λ x, x + 2 y + z = λ y, - x - y - λ z = 0$ has a non-trivial solution is