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).`

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

Solve the system of the equations: a x+b y+c z=d , a^2x+b^2y+c^2z=d^2 , a^3x+b^3y+c^3z=d^3 .

if x,y and z are not all zero and connected by the equations a_(1)x+b_(1)y+c_(1)z=0,a_(z)x+b_(2)y+c_(2)z=0 and (p_(1)+lambdaq_(1))x+(p_(2)+lambdaq_(2))y+(p_(3)+lambdaq_(3))z=0 show that lambda =-|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(p_(1) ,, p_(2),,p_(3)):}|-:|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(q_(1) ,, q_(2),,q_(3)):}|

Solve the following system of equations by using determinants: x+y+z=1 , a x+b y+c z=k , a^2x+b^2y+c^2z=k^2

Solve the following system of equations by using determinants: x+y+z=1 , a x+b y+c z=k , a^2x+b^2y+c^2z=k^2 .

If x,y,z are in G.P and a^x=b^y=c^z ,then

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

STATEMENT-1 : If a, b, c are distinct and x, y, z are not all zero and ax + by + cz = 0, bx + cy + az = 0, cx + ay + bz = 0 , then a + b + c = 0 and STATEMENT-2 : a^2 + b^2 + c^2 > ab + bc + ca , if a, b, c are distinct.

If the foot of the perpendicular from the origin to plane is P(a ,b ,c) , the equation of the plane is a. x/a=y/b=z/c=3 b. a x+b y+c z=3 c. a x+b y+c z=a^(2)+b^2+c^2 d. a x+b y+c z=a+b+c

If a, b, c are non - zero real numbers, the system of equations y+z=a+2x, x+z=b+2y, x+y=c+2z is consistent and b=4a+(c )/(4) , then the sum of the roots of the equation at^(2)+bt+c=0 is