A set of values of for which the system of equations ( 3 ) x-y+z=0 , ( 2 ) x+4 y+3 z=0,2 x+7 y+7 z=0 has non-trivial solutions, is

Step-by-step solution

For non-trivial solution, =0 | array ccc 3 & -1 & 1 2 & 4 & 3 2 & 7 & 7 array |=0 On expanding, aligned & 3 (28-21)+1(7 2 -6) & +1(7 2 -8)=0 & 7 3 +14 2 -14=0 & 3 +2 2 -2=0 & 3 -4 ^3 -2(1- 2 )=0 & 3 -4 ^3 -4 ^2 =0 & - (4 ^2 +4 -3 )=0 & aligned aligned & =0, 4 ^2 +4 -3=0 & =0, (2 -1)(2 +3)=0 & =0, = 1 2 [2 +3 0] & =n , =n +(-1)^n 6 . aligned