Assertion and reason: cofactors

Exercise and reference answers

Questions

1. Reason

   That sum is the expansion of a determinant with a repeated row.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Mixing a row with another row's cofactors gives zero.

2. Reason

   The adjoint is defined as the transpose of the cofactor matrix.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   adj A must be transposed after building the cofactors.

3. Reason

   A cofactor carries the sign (−1)^(i+j).

   Verdict

   Both are true; the reason does not explain the assertion.

   Assertion

   A determinant can be expanded along any row.

Explanation