Gaussian elimination and row-echelon form

Develop Gaussian elimination from legal row operations to row-echelon form and back-substitution. Practice includes pivot selection, zero-row placement, triangular systems and consistency checks, with both single-select and multiselect questions. The stated row-echelon convention permits nonunit leading entries, keeping form recognition separate from reduced row-echelon form. Worked explanations track coefficients and constants, distinguish contradictions from redundant equations, and verify the resulting solutions. The progression favors understanding the algorithm and its limitations over lengthy arithmetic.