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The three cases of a linear system

The questions ask you to read a reduced system and say which of the three outcomes holds, and to resist deciding it from the shape of the original. Elimination returns readily; telling redundancy from contradiction, and describing a set rather than a point, is what needs practice.

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What this covers

  • Say which of the three cases a reduced system falls into

    Given a system in reduced form, the learner can determine whether it has no solution, exactly one, or infinitely many, justify the verdict from the pivot structure, and for the infinite case describe the solution set rather than one member of it.

  • Reduce a linear system by elimination

    Given A x = b with explicit coefficients, the learner can apply row operations that preserve the solution set, reach echelon form without arithmetic error, and say why each operation leaves the solutions unchanged.

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