True or false: cofactor expansion

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   |A| = a₁₁A₁₁ + a₁₂A₁₂ + a₁₃A₁₃.

2. Statement is true

   Yes

   Statement

   a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃ = 0.

3. Statement is true

   Yes

   Statement

   A determinant may be expanded along any row or column.

4. Statement is true

   No

   Statement

   A minor and its cofactor are always equal.

5. Statement is true

   No

   Statement

   Mixing a row with another row's cofactors gives |A| again.

Explanation