4.2-06 Minors and cofactors

Minors and Signed Cofactors

Develop precise control of matrix indexing and cofactor signs. Practice deleting the correct row and column, evaluating the remaining determinant and placing the checkerboard sign. Later questions connect cofactors to changes in a single matrix entry.

What you will practise

• Identify the correct deleted row and column.
• Distinguish an unsigned minor from its signed cofactor.
• Calculate cofactors in small and diagonal matrices.
• Reason about which cofactors stay fixed when an entry changes.

Prerequisites and study approach

Useful preparation: Two-by-two determinants, matrix indices and triangular structure. Work through the questions from foundational interpretation to more demanding applications. Both single-select and multiselect items are included; in a multiselect item, judge every statement independently. Try a calculation, sketch or short justification before consulting the explanation.

The worked feedback develops the reasoning and addresses common errors such as transposing indices too early, applying the sign twice or assuming a zero entry must have a zero cofactor. Use it to compare your method with the stated assumptions, then revisit any step you could not justify. This microlearning belongs to Module 4, Determinants, Volume and Orientation, in the Complete Linear Algebra Course.