`x+a y+a^2z=0+b y+b^2z=0+c y+c^2z=0!=b!=c` then given system of equations

x+ay+az=0,x+by+b^(2)z=0,x+cy+c^(2)z=0,a!=b!=c then given system of equations

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

Statement I: If a ,\ \ b , c in R\ a n d a!=b!=c\ a n d\ x ,\ y ,\ z are non zero. Then the system of equations a x+b y+c z=0b x+c y+a z=0c x+a y+b z=0 has infinite solutions. because Statement II: If the homogeneous system of equations has no non trivial solution, then it has infinitely many solutions. a. A b. \ B c. \ C d. D

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

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

If x=a,y=b,z=c is a solution of the system of linear equations x+8y+7z=0,9x+2y+3z=0,x+y+z=0 such that the point (a,b,c) lies on the plane x+2y+z=6, then 2a+b+c equal to

Show that |a b c a+2x b+2y c+2z x y z|=0

Show that |a b c a+2x b+2y c+2z x y z|=0

If the system of equations x - 2y +z = a , 2x + y - 2z = b, x +3y - 3z = c, has at least one solution, then a) a + b + c = 0 b) a - b + c = 0 c) -a + b + c = 0 d) a + b - c = 0