Suppose a, b and c are distinct and x,y and z are connected by the system of eqationsx+ay+a^(2)z...

Suppose a, b and c are distinct and x,y and z are connected by the system of eqations x+ay+a^(2)z=a^(3),x+by+b^(2)z=b^(3) "and" x+cy+c^(2) z=c^(3).

Suppose that three points z_(1), z_(2), z_(3) are connected by the relation a z_(1) + b z_(2) + c z_(3) = 0 , where a + b + c = 0, then the points are

Examine the consistency of the system of equations x2x+3y+2z=2ax+ay+quad 2aquad z=4

If the system of equations ax + by + c = 0,bx + cy +a = 0, cx + ay + b = 0 has infinitely many solutions then the system of equations (b + c) x +(c + a)y + (a + b) z = 0(c + a) x + (a+b) y + (b + c) z = 0(a + b) x + (b + c) y +(c + a) z = 0 has

The number of distinct real values of lamda for which the system of linear equations x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z has non - trival solution.

If x,z and y are in A.P.where x,y and z are distinct numbers then evaluate (x)/(x-z)+(z)/(y-z)

The system of equations -2x+y+z=a x-2y+z=b x+y-2z=c has

If n is an odd positive integer and x,y,z are distinct then the number of distinct terms in the expansion of (x+y+z)^(n)+(x-y-z)^(n) is

If S is the set of distinct values of 'b for which the following system of linear equations x+y+z=1x+ay+z=1ax+by+z=0 has no solution,then S is : a finite set containing two or more elements ( 2) a singleton an empty set (4) an infinite set