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`

The system of equations x+2y-4z=3,2x-3y+2z=5 and x -12y +16z =1 has

consider the system of equations : ltbr. 3x-y +4z=3 x+2y-3z =-2 6x+5y+lambdaz =-3 Prove that system of equation has at least one solution for all real values of lambda .also prove that infinite solutions of the system of equations satisfy (7x-4)/(-5)=(7y+9)/(13)=z

If system of equation x + y + z = 6 x + 2y + 3z = 10 3x + 2y + lambda z = mu has more than two solutions. Find (mu -lambda )

For the system of equations: x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

If system of equation x + y + z = 6 ,x + 2y + 3z = 10, 3x + 2y + lambda z = mu has more than two solutions. Find (mu -lambda^2 )

Show that the homogenous system of equations x - 2y + z = 0, x + y - z = 0, 3 x + 6y - 5z = 0 has a non-trivial solution. Also find the solution

Examine the consistency of the system of equations 3x -y - 2z = 2" " 2y -z = 1" " 3x - 5y = 3

If the system of linear equation x+y+z=6,x+2y+3c=14 ,a n d2x+5y+lambdaz=mu(lambda,mu R) has a unique solution, then

If the system of equations x+y+z=2 2x+4y-z=6 3x+2y+lambdaz=mu has infinitely many solutions, then :

If the system of equations x + 2y + 3z = 4, x+ py+ 2z = 3, x+ 4y +u z = 3 has an infinite number of solutions and solution triplet is