For a real number a, if the system `{:[(1,a,a^2),(a,1,a),(a^2,a,1)][(x),(y),(z)]=[(1),(-1),(1)]:}`
of the linear equations, has infinitely many solutions, then `1+a+a^2=`

For a real number alpha, if the system [1alphaalpha^2alpha1alphaalpha^2alpha1][x y z]=[1-1 1] of linear equations, has infinitely many solutions, then 1+alpha+alpha^2=

For a real number alpha, if the system [1alphaalpha^2alpha1alphaalpha^2alpha1][x y z]=[1-1 1] of linear equations, has infinitely many solutions, then 1+alpha+alpha^2=

For a real number, alpha if the system [{:(,1,alpha,alpha^(2)),(,alpha,1,alpha),(,alpha^(2),alpha,1):}] [{:(,x),(,y),(,z):}]=[{:(,1),(,-1),(,1):}] of linear equations has infinitely many solutions then 1+alpha+alpha^(2) =

For a real number alpha, if the system [[1,alpha,alpha^2],[alpha,1,alpha],[alpha^2,alpha,1]][[x],[ y], [z]]=[[1],[-1],[1]] of linear equations, has infinitely many solutions, then 1+alpha+alpha^2=

For a real number, alpha if the system [{:(,1,alpha,alpha^(2)),(,alpha,1,alpha),(,alpha^(2),alpha,1):}] [{:(,x),(,y),(,z):}]=[{:(,1),(,-1),(,1):}] of linear equations has infinitely many solutions then 1+alpha+alpha^(2) =

For real numbers alpha and beta , consider the following system of linear equations: x+y-z=2, x+2y+alpha z=1, 2x- y+z= beta . If the system has infinite solutions, then alpha+beta is equal to ____

Solve the system of equations using matrix method. x+y+z=1 , 2x+3y-z=6 , x-y+z=-1

If x,y,z are distinct real numbers then the value of ((1)/(x-y))^(2)+((1)/(y-z))^(2)+((1)/(z-x))^(2) is

If a, b and c are non - zero real numbers and if system of equations (a-1)x=y+z, (b-1)y=z+x and (c-1)z=x+y have a non - trivial solutin, then (3)/(2a)+(3)/(2b)+(3)/(2c) is equal to

If a, b and c are non - zero real numbers and if system of equations (a-1)x=y+z, (b-1)y=z+x and (c-1)z=x+y have a non - trivial solutin, then (3)/(2a)+(3)/(2b)+(3)/(2c) is equal to