Consider the system of equations $$ax+by+cz=2$$,$$bx+cy+az=2$$,$$cx+ay+bz=2where$$ a,b,c are real numbers such that $$a+b+c=0then$$ the system

Question

Consider the system of equations $$ax+by+cz=2$$,$$bx+cy+az=2$$,$$cx+ay+bz=2where$$ a,b,c are real numbers such that $$a+b+c=0then$$ the system

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Augmented matrix $$AD=abc2bca2cab2$$                                               $$R3$$→$$R1+R2+R2$$                                          ~$$abc2bca2a+b+ca+b+ca+b+c6$$                                           ~$$abc2bca20006$$ ∵$$a+b+c=0Here$$ $$rankA=2$$ and $$rankAD=3$$∴rankA≠rankAD The given system is inconsistent

Consider the system of equations $a x + b y + c z = 2, b x + c y + a z = 2, c x + a y + b z = 2$ where a,b,c are real numbers such that $a + b + c = 0$ then the system

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Consider the system of equations ax+by+cz=2,bx+cy+az=2,cx+ay+bz=2where a,b,c are real numbers such that a+b+c=0then the system

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Consider the system of equations $a x + b y + c z = 2, b x + c y + a z = 2, c x + a y + b z = 2$ where a,b,c are real numbers such that $a + b + c = 0$ then the system