Show that the system of equations `3x-y + 4z = 3, x + 2y-3z =-2` and `6x + 5y + lambdaz=-3` has at least one solution for any real number `lambda.` Find the set of solutions of `lambda =-5`

If the system of equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + alphaz = beta has infinitely many solution, then beta - alpha equals

The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2x + 3y + (a^(2) - 1)z = a + 1

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

Examine the consistency of the system of equations 5x-y+4z =5 2x+ 3y + 5z =2 5x-2y + 6z =-1

If the system of equations x+y+z=6, x+2y+kz=0 and x+2y+3z=10 has no solution, then the value of k is -

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

The system of linear equations x+lambday-z=0 , lambdax-y-z=0 , x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

The value of k for which the system of equations x+ky-3z=0 , 3x+ky-2z=0, 2x+3y-4z=0 has a non -trivial solution is

The system of equation x+y+2z=1, x+2y+3z=2, x+4y+alphaz=4 . Has unique then