For what value of `k` the following system of linear equations wil have infinite solutions `x-y+z=3, 2x+y-z=2` and `-3x-2ky+6z=3`

Show that the following systems of linear equations has infinite number of solutions x-y+z=3,\ \ \ 2x+y-z=2,\ \ -x-2y+2z=1

Show that the following systems of linear equations has infinite number of solutions and solve x-y+z=3,\ \ \ 2x+y-z=2,\ \ -x-2y+2z=1

Find the real values of k for which the following system of linear equations has non-trivial solutions: x-ky+z=0,kx+3y-kz=0,3x+y-z=0

Find the real values of K for which the following system of linear equations has non-trival solutions: x-ky+z = 0, kx + 3y - kz = 0, 3x + y-z = 0

Show that the following systems of linear equations has infinite number of solutions and solve x-y+3z=6,\ \ x+3y-3z=-4,\ \ 5x+3y+3z=10

Show that the following systems of linear equations has infinite number of solutions and solve x-y+3z=6,\ \ x+3y-3z=-4,\ \ 5x+3y+3z=10

Show that the following systems of linear equations are inconsistent: 3x-y+2z=6,\ \ 2x-y+z=2,\ \ 3x+6y+5z=20.

Show that the following systems of linear equations has infinite number of solutions and solve 2x+y-2z=4,\ \ x-2y+z=-2,\ \ 5x-5y+z=-2

Show that the following systems of linear equations has infinite number of solutions and solve 2x+y-2z=4,\ \ x-2y+z=-2,\ \ 5x-5y+z=-2

Show that the following systems of linear equations are consistent: 3x-y+2z=6,\ \ 2x-y+z=2,\ \ 3x+6y+5z=20.