[" 31.The set of all values of "lambda" fur atich the sysiem of linerer "],[[" cquations: "],[qquad [2x_(1)-2x_(2)+x_(3)=lambda x_(1)],[2x_(1)-3x_(2)+2x_(3)=lambda x_(2)],[-x_(1)+2x_(2)=lambda x_(3)]]]

The set of all values of lambda for which the system of linear equations 2x_(1)-2x_(2)+x_(3)=lambda x_(1), 2x_(1)-2x_(2)+2x_(3)=lambda x_(2), -x_(1)+2x_(2)=lambdax_(3) has a non-trivial solution

The set of all values of lambda for which the system of linear equations 2x_(1)-2x_(2)+x_(3)=lambdax_(1) 2x_(1)-3x_(2)+2x_(3)=lambdax_(2) -x_(1)+2x_(2)=lambdax_(3) has a non-trivial solution,

The set of all values of lambda for which the system of linear equation |(2x_(1)-2x_(2)+x_(3),=lambdax_(1)),(2x_(1)-3x_(2)+2x_(3),=lambdax_(2)),(-x(1)+2x_(2),=lambdax_(3))| has a non trivial solution

The set of all values of lambda for which the system of linear equations: 2x_(1)-2x_(2)+x_(3)=lambda x_(1)2x_(1)-3x_(2)+2x_(3)=lambda x_(2) has a non-trivial solution,(1) is an empty set (2) is a singleton ( 3) contains two elements (4) contains more than two elements

Let lambda in R . The system of linear equations 2x_(1) - 4x_(2) + lambda x_(3) = 1 x_(1) -6x_(2) + x_(3) = 2 lambda x_(1) - 10x_(2) + 4 x_(3) = 3 is inconsistent for :

Let lambda in R , the system of linear equation 2x_1-4x_2+lambdax_3=1 x_1-6x_2+x_3=2 lambda x_1-10x_2+4x_3=3 is inconsistant. Find the value of lambda .

The sum of distinct value of lambda for which the system of equations (lambda -1 )x + (3lambda + 1) y + 2 lambda x= 0 (lambda -1) x + (4lambda - 2) y + (lambda + 3) x= 0 2x + (2lambda + 1) y + 3(lambda - 1) z=0 has non - zeor solutions is ______.

Determine the values of lambda for which the following system of equations: lambda x+3y-z=1x+2y+z=2-lambda x+y+2z=-1 has non-trival solutions.

The number of distinct real values of lambda for which the lines (x-1)/(1)=(y-2)/(2)=(z+3)/(lambda^(2)) and (x-3)/(1)=(y-2)/(lambda^(2))=(z-1)/(2) are coplanar is

If x_(1)+x_(2)=(pi)/(2) and x_(2)+x_(3)=x_(1), then tan x_(1)=tan x_(2)+lambda tan x_(3) where lambda is equal to