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` Will the solution always exist and be unique?

Solve the system of equations by cramer's rule: x+y+z=3 , 2x-y+3z=4 and x+2y-z=2

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

Suppose the system of equations a_(1)x+b_(1)y+c_(1)z=d_(1) a_(2)x+b_(2)y+c_(2)z=d_(2) a_(3)x+b_(3)y+c_(3)z=d_(3) has a unique solution (x_(0),y_(0),z_(0)) . If x_(0) = 0 , then which one of the following is correct ?

Consider the system of equation x+2y-3z=a , 2x+6y-11z=b , x-2y+7c then

Solve the system of equations : z+ay+a^(2)x+a^(3)=0z+by+b^(2)x+b^(3)=0z+cy+c^(2)x+c^(3)=0] where a!=b!=c

The solution of the system of equations a_(1)x+b_(1)y+c_(1)z=d_(1),a_(2)x+b_(2)y+c_(2)z=d_(2) and a_(3)x+b_(3)y+c_(3)z=d_(3) using Crammer's rule is x=(Delta_(1))/(Delta),y=(Delta_(2))/(Delta) and z=(Delta_(3))/(Delta) where Delta!=0 The solution of the system 2x+y+z=1 , x-2y-z=(3)/(2) , 3y-5z=9 is