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 `"____"`

The number of real values of alpha for which the system of equations {:(x+3y+5z=alphax),(5x+y+3z=alpha y),(3x+5y+z= alpha z):} has infinite number of solutions is

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0, alphax+(alpha+b)y+alphaz=0, alphax+alphay+(alpha+c)z=0 has a non-trivial solution if

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0,alphax+(alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0' has a non-trivial solution if alpha^(-1)= (A) -(a^(-1)+b^(-1)+c^(-1)) (B) a+b+c (C) alpha+a+b+c=1 (D) none of these

An ordered pair (alpha, beta) for which the system of linear equations (1+alpha)x+betay+z=2 , alphax+(1+beta)y+z=3 and alphax+betay+2z=2 has unique solution is: (a) (2,4) (b) (-3,1) (c) (-4,2) (d) (1,-3)

The system of equation x+y+2z=1, x+2y+3z=2, x+4y+alphaz=4 . Has unique then

If the system of equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + alphaz = beta has infinitely many solution, then beta - alpha equals

Find the range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution.

If x alpha 1/y then

If one root of the equation (alpha-4)x^2+2x+1=0 is 1, then alpha =

If x+y alpha x-y then