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) =

Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2dot

The equation sin^(-1)x=2sin^(-1)alpha has a solution

The system of equations alpha x + y + z = alpha - 1 x + alpha y + = alpha - 1 , x + y + alpha z = alpha - 1 has infinite solutions, if alpha is

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 ____

If the system of linear equations {:(2x+y-z=3),(x-y-z=alpha),(3x+33y-betaz=3):} has infinitely many solution, then alpha+beta-alphabeta is equal to ______.

10/Find the value of alpha and beta for which the following system of linear equations has infinite number of solutions 2x+3y=7,2 alpha x+(alpha+beta)y=28

Find the values of alpha and beta for which the following system of linear equations has infinite number of solutions: 2x+3y=7,quad 2 alpha x+(alpha+beta)y=28