Let and be real array r x+ y+ z=0 x+ y+ z=0 -x+ y- z=0 array has a non-trivial solution. If =1 , then all the values of is equals

Step-by-step solution

The given system has a non-trivial solution, if | array rrr & & 1 & & -1 & & - array |=0 By expanding the determinant along ( C₁ ), we get gathered (- ^2 - ^2 )-1(- - ) -1 ( ^2 - ^2 )=0 = 2 + 2 gathered For =1, 2 + 2 =1 1 2 2 + 1 2 2 = 1 2 (2 - 4 )= (2 n 4 ) 2 =2 n 4 + 4 , n being an integer. =n + 4 , n