The value of `|alpha|` for which the system of equation
`alphax+y+z=alpha-1`
`x+alphay+z=alpha-1`
`x+y+alphaz=alpha-1`
has no solution , is `"____"`

Answer

2

Explanation

System of equation
`alpha x +y+ z=alpha-1`
`x+alpha y+z = alpha-1 `
`x+y +alpha z =alpha -1`
Since system has no solution
Therefore (1) `Delta =0` and (2) `alpha -1 ne 0`
`|{:(alpha,,1,,1),(1,,alpha,,1),(1,,1,,alpha):}|= 0, alpha ne 1`
`R_(1) to R_(1) -R_(3),R_(2) to R_(2)-R_(3)`
` |{:(alpha-1,,0,,1-alpha),(0,,alpha-1,,1-alpha),(1,,1,,alpha):}|=0`
`" or " (alpha-1 )[alpha(alpha-1)-(1-alpha)]+(-alpha)[-(alpha-1)]=0`
`" or " (alpha-1 )[alpha(alpha-1)+(alpha-1)]+(alpha-1)^(2)=0`
`" or " (alpha-1)^(2)[(alpha+1)+1]=0`
`" or " alpha=1 ,1, -2 " or " alpha =1,-2`
Sicne system has no solution `alpha ne 1`
`:. alpha=-2`