Determinants, singularity and Cramer's rule

Build confidence with determinants, singular matrices and Cramer's rule in this precalculus extension practice. Work from small determinant calculations and cofactor signs to column replacement, parameter restrictions and solution classification. Single-select and multiselect questions combine conceptual checks, worked calculations and error analysis. Detailed explanations show why nonzero determinants matter and how substitution verifies a solution. Prior knowledge of matrix multiplication, inverses and linear systems is recommended; lengthy higher-order expansions are not required.