Augmented matrices and elementary row operations

Understand augmented matrices as compact representations of linear systems. Starting with variable order and missing coefficients, this precalculus practice set develops row swaps, nonzero row scaling and row replacement through concrete calculations. Single-select and multiselect problems distinguish reversible equation operations from changes that lose information or alter the solution set. Detailed explanations track the constant column and show how to undo a legal operation. The focus is accurate representation and justified steps, preparing learners for Gaussian elimination rather than requiring full row reduction in advance.