If the system of equations λ$$x1+x2+x3=1$$, $$x1+$$λ$$x2+x3=1$$, $$x1+x2+$$λ$$x3=1$$ is inconsistent, then λ$$=$$ $$___________$$

Question

If the system of equations λ$$x1+x2+x3=1$$, $$x1+$$λ$$x2+x3=1$$,  $$x1+x2+$$λ$$x3=1$$ is inconsistent, then λ$$=$$ $$___________$$

Infinity Learn · Accepted Answer

The necessary condtion for a $$non-homogeneous$$ system of equations to be inconsistent is Δ$$=0$$ ⇒λ$$111$$λ$$111$$λ$$=0$$      $$C1$$→$$C1+C2+C2$$   $$=$$λ$$+211$$λ$$+2$$λ$$1$$λ$$+21$$λ    $$=$$λ$$+21$$    $$1$$     $$11$$    λ    $$11$$      $$1$$    λ          $$R1$$→$$R1$$−$$R2$$:, $$R2$$→$$R2$$−$$R3$$      $$=$$λ$$+20$$   $$1$$−λ   $$00$$    λ−$$1$$  $$1$$−λ$$1$$        $$1$$                  λ       $$=$$λ$$+20$$λλ$$-1-1-$$λ−$$1$$−λ$$0$$−$$1$$−λ$$=$$λ$$+21$$−λ$$2=0$$⇒λ$$=$$−$$2$$,$$1$$

If the system of equations $λ x_{1} + x_{2} + x_{3} = 1, x_{1} + λ x_{2} + x_{3} = 1, x_{1} + x_{2} + λ x_{3} = 1$ is inconsistent, then $λ =$ ___________

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If the system of equations λx1+x2+x3=1, x1+λx2+x3=1, x1+x2+λx3=1 is inconsistent, then λ= ___________

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Ready to Test Your Skills?

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If the system of equations $λ x_{1} + x_{2} + x_{3} = 1, x_{1} + λ x_{2} + x_{3} = 1, x_{1} + x_{2} + λ x_{3} = 1$ is inconsistent, then $λ =$ ___________