Show that the equations -2x+y+z=a,x-2y+z=b,x+y-2z=c are consistent only if a+b+c=0.

Show that the equations: x+y+z=6,x+2y+3z=14,x+4y+7z=30 are consistent and solve them.

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

The system of equations -2x+y+z=a , x-2y+z=b , x+y-2z=c , has: (a)no solution if a+b+c!=0 (b)unique solution if a+b+c=0 (c)infinite number of solutions if a+b+c=0 (d)none of these

(a) Show that the equations x +y +z = 6 , x + 2y + 3z = 14 , x + 4y + 7z = 30 are consistent and solve them .

Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-5y+4z=lambda is consistent and find the solutions for all such values of lambdadot

Show that the equations 3x+y+9z=0, 3x+2y+12z=0 and 2x+y+7z=0 have non-trival solutions also.

The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

Find k if the equations x+2y+2z=0, x-3y-3z=0, 2x+y+kz=0 have only the trivial solution.

If the system of equation {:(,x-2y+z=a),(2x+y-2z=b),and,(x+3y-3z=c):} have at least one solution, then

If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=c where a,b and c are non-zero real numbers, has more than one solution, then