If `2a x-2y+3z=0,x+a y+2z=0,a n d2+a z=0` have a nontrivial solution, find the value of `adot`

If the system of equations 3x-2y+z=0, lambda x-14y+15z=0, x+2y+3z=0 have a non trivial solution, then the value of lambda^(2) must be

If 4x-ay+3z=0, x+2y+ax=0 and ax+2z=0 have a non - trivial solution, then the number of real value(s) of a is

The equations x+ky+3z=0,3x+ky-2z=0,2x+3y-4z=0 possess a nontrivial solution then the value of (2k)/33 is

x-2y+z=0 y-z=2 2x-3z=10

If system of homogenous equations x+ky-2z=0,2x+y-3z=0 and 4x+2y-kz=0 has non-trivial solution thenthe integral value of k is

if the system of equations x+y+z=0 , x+3y+k^2z=0 and x+2y+z=0 have a non zero solution then value of y+(x/z) is

If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

the value of theta for which the system of equations (sin 3theta)x-2y+3z=0, (cos 2theta)x+8y-7z=0 and 2x+14y-11z=0 has a non - trivial solution, is (here, n in Z )

Find a in R for which the system of equations 2ax-2y+3z=0 , x+ay + 2z=0 and 2x+az=0 also have a non-trivial solution.