4.2-07 Cofactor expansion

Cofactor Expansion and Efficient Row Selection

Practice cofactor expansion as both a computational method and a proof tool. The set emphasizes sparse rows and columns, signed contributions and useful checks against another expansion. More demanding questions connect expansion with parameter changes and repeated-row identities.

What you will practise

• Choose a sparse row or column for expansion.
• Combine entries with the correct signed cofactors.
• Evaluate three-by-three and sparse four-by-four examples.
• Explain mismatched cofactor sums and single-entry changes.

Prerequisites and study approach

Useful preparation: Minors, cofactors, determinant signs and elementary algebra. 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 applying a second checkerboard sign to an already signed cofactor or multiplying a row by cofactors from the wrong row. 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.