If | array ccc a & -b & a-b-c -a & b & -a+b-c -a & -b & -a-b+c array |-k a b c=0 (a 0, b 0, c 0) then what is the value of k ?

Step-by-step solution

aligned & Applying c₃ c₃-c₁-c₂ & | array ccc a & -b & -c -a & b & -c -a & -b & c array |-k a b c=0 & a b c-k a b c=0 & Applying R₂ R₂+R₁ and R₃ R₃+R₁ & a b c | array ccc 1 & -1 & -1 -1 & 1 & -1 -1 & -1 & 1 array |-k a b c=0 & -4 a b c-k a b c=0 & k=-4 aligned