The greatest value of c∈R for which the system of linear equations x−cy−$$cz=0$$,cx−$$y+cz=0$$,$$cx+cy$$−$$z=0$$ has a non – trivial solution , is

Question

The greatest value of c∈R for which the system of linear equations x−cy−$$cz=0$$,cx−$$y+cz=0$$,$$cx+cy$$−$$z=0$$  has a non – trivial solution , is

Infinity Learn · Accepted Answer

Given system of linear equations is x−cy−$$cz=0cx$$−$$y+cz=0$$ And $$cx+cy$$−$$z=0We$$ know that a homogeneous system of linear equations have $$non-trivial$$ solutions if Δ$$=0$$⇒$$1$$−c−cc−$$1ccc$$−$$1=0$$⇒$$11$$−$$c2+c$$−c−$$c2$$−$$cc2+c=0$$⇒ $$1$$−$$c2$$−$$c2$$−$$c3$$−$$c3$$−$$c2=0$$⇒ −$$2c3$$−$$3c2+1=0$$⇒ $$2c3$$−$$3c2$$−$$1=0$$⇒ $$(c+1)2c2+2c$$−c−$$1=0$$⇒ $$(c+1)(2c$$−$$1)(c$$−$$1)=0$$⇒ $$c=$$−$$1$$ or $$12$$ Clearly $$_$$ the greatest value of c is $$12$$.

The greatest value of $c \in R$ for which the system of linear equations $x - c y - c z = 0, c x - y + c z = 0, c x + c y - z = 0$ has a non – trivial solution , is

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The greatest value of c∈R for which the system of linear equations x−cy−cz=0,cx−y+cz=0,cx+cy−z=0 has a non – trivial solution , is

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The greatest value of $c \in R$ for which the system of linear equations $x - c y - c z = 0, c x - y + c z = 0, c x + c y - z = 0$ has a non – trivial solution , is