[" (viii) "2x+3y+3z=5;x-2y+z=-4;3x-y-2z=3],[" C.E.R.T.; H.B.2014; Jammu B.2013; H.P.B.2010S) "]

x+y+z=1 x-2y+3z=2 5x-3y+z=3

2x-y+z=6,x+2y+3z=3,3x+y-z=4

2x-3y+5z=16, 3x+ 2y-4z= -4, x + y - 2z =- 3.

5x-[4y-{7x-(3z-2y)+4z-3(x+3y-2z)}]

The system 2x + 3y + z= 5, 3x + y + 5z =7, x + 4y -2z=3 has

If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z are in a. A.P. b. G.P. c. H.P. d. none of these

If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z are in a. A.P. b. G.P. c. H.P. d. none of these

If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z are in a. A.P. b. G.P. c. H.P. d. none of these

Let S be the set of all column matrices [b_1b_2b_3] such that b_1,b_2, b_3 in R and the system of equations (in real variable) -x+2y+5z=b_1 2x-4y+3z=b_2 x-2y+2z=b_3 has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each [b_1b_2b_3] in S? (a) x+2y+3z=b_1, 4y+5z=b_2 and x+2y+6z=b_3 (b) x+y+3z=b_1, 5x+2y+6z=b_2 and -2x-y-3z=b_3 (c) -x+2y-5z=b_1, 2x-4y+10 z=b_2 and x-2y+5z=b_3 (d) x+2y+5z=b_1, 2x+3z=b_2 and x+4y-5z=b_3