Statement 1: If the system of equation `lambdax+(b-a)y+(c-a)z=0,(a-b)x+lambday+(c-b)z=0,a n d(a-c)x+(b-c)y+lambdaz=0` has a non trivial solution, then the value of `lambda` is 0.
Statement 2: the value of skew symmetric matrix of order 3 is Zero.

If p q r!=0 and the system of equation (p+a)x+b y+c z=0 , a x+(q+b)y+c z=0 , a x+b y+(r+c)z=0 has nontrivial solution, then value of a/p+b/q+c/r is a. -1 b. 0 c. 1 d. 2

The system of linear equations x+lambday-z=0 , lambdax-y-z=0 , x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

Find the real values of a for which the system of equations a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0 x+y+z=0 has a non -zero solution.

Find the value of lambda for which the homogeneous system of equations: 2x+3y-2z=0 , 2x-y+3z=0 , 7x+lambday-z=0 has non-trivial solutions.

If a ,b ,c are non -zero real numbers and if the system of equations (a-1) x=y+z,(b-1)y=z+x,(c-1) z=x+y has a non -trivial solution, then prove that ab+bc+ca =abc .

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are a. -1,2 b. 1,2 c. 0,1 d. -1,1

The set of all values of lambda for which the system of linear equations x - 2y - 2z = lambdax x + 2y + z = lambday -x -y = lambdaz has a non-trivial solution

Statement 1: "Delta"= |[m y+n z, m q+n r, m b+n c],[k z-m x, k r-m p, k c-m a],[-n x-k y,-n p-k q,-n a-k b]| is equal to 0. Statement 2: The value of skew symmetric matrix of order 3 is zero.

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

Find the number of values of lambda for which the system of equations lambdax+y+z=1,x+lambday+z=lambda and x+y+lambdaz=lambda^2 has infinite number of solutions .