Question

The system of equations αx + y + z = α – 1, x + αy + z = α – 1, x + y +αz = α – 1 has no solutions,

Answer 1

=ax+y+z=a-1.............(1)
=x+ay+z=a-1..............(2)
=x+y+az=a-1..............(3)
eqs...........(1)+(2)+(3)
=a(x+y+z)+2(x+y+z)=3a-3
=a(x+y+z)-2(-x-y-z)=3a-3
=By Comparing........
=x+y+z=3........(4)
=-x-y-z=3
=x+y+z=-3.........(5)
eqs........(4)+(5)
=2x+2y+2z=3-3
=2x+2y+2z=0
=x+y+z=0. Answer