The system of equations α$$x+y+z=$$α−$$1$$, $$x+$$α$$y+z=$$α−$$1$$, $$x+y+$$α$$z=$$α−$$1$$ has no solution, if α$$=$$

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The system of equations α$$x+y+z=$$α−$$1$$, $$x+$$α$$y+z=$$α−$$1$$, $$x+y+$$α$$z=$$α−$$1$$ has no solution, if α$$=$$

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LetΔ$$=$$α$$111$$α$$111$$α              $$C1$$→$$C1+C2+C3$$          $$=$$α$$+211$$α$$+2$$α$$1$$α$$+21$$α         $$=($$α$$+2)$$ $$1111$$α$$111$$α                $$R1$$→$$R1$$−$$R2$$, $$R2$$→$$R2$$−$$R3$$        $$=($$α$$+2)01-$$α$$00$$α$$-11-$$α$$11$$α $$=$$α$$+2o($$αα$$-1-11-$$α$$)$$−(1$$−α$$)0$$−$$(1$$−α$$)         $$=($$α$$+2)(1$$−α$$)2If$$ α$$=1the$$ system of equations has infinitely many solutions If α$$=$$−$$2$$, on adding $$3$$ equations we obtain $$0=-9$$∴ The system has no solution for α$$=$$−$$2$$

The system of equations $α x + y + z = α - 1, x + α y + z = α - 1, x + y + α z = α - 1$ has no solution, if $α =$

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The system of equations αx+y+z=α−1, x+αy+z=α−1, x+y+αz=α−1 has no solution, if α=

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The system of equations $α x + y + z = α - 1, x + α y + z = α - 1, x + y + α z = α - 1$ has no solution, if $α =$