Question

2. a—b b—c c—a b—c c a a—b=0 c—a a b b—c

Answer 1

The given matrix is,

[ a−b b−c c−a b−c c−a a−b c−a a−b b−c ]

Determinant of the given matrix is,

Δ=| a−b b−c c−a b−c c−a a−b c−a a−b b−c |

Apply row operation, R 1 → R 1 +R 2 +R 3 .

Δ=| a−b+b−c+c−a b−c+c−a+a−b c−a+a−b+b−c b−c c−a a−b c−a a−b b−c | =| 0 0 0 b−c c−a a−b c−a a−b b−c |

From the determinant property, if any row or column of a determinant has zero element, then value of the determinant is zero.

In the above determinant, row R 1 has zero identities.

Thus, the value of the determinant is 0.