Statement-1: The system of linear equations aligned & x+( ) y+( ) z=0 & x+( ) y+( ) z=0 & x-( ) y-( ) z=0 aligned has a non-trivial solution for only one value of lying in the interval (0, 2 ) . Statement-2: The equation in | array ccc & & & & & - & - array |=0 has only one solution lying in the interval (0, 2 )

Step-by-step solution

aligned & = 64 x 3 16 x = 4 3 & ₁= | array ccc 1 & & 1 & & 1 & - & array | & = | array ccc 0 & - & - 0 & + & - 1 & - & array | & =( - )^2- ( ^2 - ^2 ) & = ^2 + ^2 -2 - ^2 & =2 ^2 -2 & =2 ^2 ( - ) aligned Now, - =0 for only aligned & = 4 in (0, 2 ) ₁ & =2( ) 0=0, aligned since value of is finite for (0, 2 ) Hence non-trivivial solution for only one value of in (0, 2 ) aligned & | array ccc & & & & & - & - array |=0 & | array ccc 0 & & 0 & & 2 & - & - array |=0 & 2 ( ^2 - ^2 )=0 & =0 or ^2 - ^2 =0 aligned But =0 not