The value of | array ccc 1 & 1 & 1 b c & c a & a b b+c & c+a & a+b array | is

Step-by-step solution

We have, | array ccc 1 & 1 & 1 b c & c a & a b b+c & c+a & a+b array | On applying C₁ C₁-C₂, C₂ C₂-C₃ , we get | array ccc 0 & 0 & 1 -c(a-b) & -a(b-c) & a b -(a-b) & -(b-c) & a+b array | Taking common (a-b),(b-c) from C₁, C₂ respectively, we get (a-b)(b-c) | array ccc 0 & 0 & 1 -c & -a & a b -1 & -1 & a+b array | On expanding along R₁ , we get aligned &(a-b)(b-c) 1(c-a) &=(a-b)(b-c)(c-a) aligned