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 :

Question

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 : (A) (3/4) (B) -4 (C) (1/2) (D)  - (1/4)

Tardigrade Admin · Accepted Answer

beginpmatrix2&3&-1 1&K&-2 2&-1&1 endpmatrix = 0 By solving K = (9/2) 2x+3y-z=0 .....(1) x+ (9/2) y-2z=0 ...(2) 2x - y + z = 0 ....(3) (1)-(3) ⇒ 4y - 2z = 0 2y = z ...(4) (y /z) = (1/2) ...(5) put z from eqn. (4) into (1) 2x + 3y - 2y = 0 2x + y = 0 (x/y) = - (1/2) ....(6) ((6)/(5)) (z/x) = - 4 (x/y) + (y/z) + (z/x) + K = (1/2)

Q. If the system of equations $2 x + 3 y - z = 0, x + k y - 2 z = 0$ and $2 x - y + z = 0$ has a non-trivial solution $(x, y, z)$ , then $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k$ is equal to :

$\frac{3}{4}$

-4

$\frac{1}{2}$

$- \frac{1}{4}$

Q. 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 yx​+zy​+xz​+k is equal to :

43​

-4

21​

−41​

Q. If the system of equations $2 x + 3 y - z = 0, x + k y - 2 z = 0$ and $2 x - y + z = 0$ has a non-trivial solution $(x, y, z)$ , then $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k$ is equal to :

$\frac{3}{4}$

$\frac{1}{2}$

$- \frac{1}{4}$