Lab · c07.s05.L1

Elimination stepper

Elimination rewrites a system without changing its solutions, and the final pivot pattern says whether there are none, one, or infinitely many.

Question: How does elimination find every solution?

Schematic Schematic: three teaching systems share one three-by-four table. Every elimination step, fraction, rank, pivot position and check line is computed exactly in rational arithmetic by data/scripts/c07.s05.L1.py, never measured. The frames walk the first system to reduced row echelon form and read off one point, then run the same coefficients with a different right-hand side to show two pivots giving a line of solutions, and a third right-hand side giving a zero row with a nonzero entry, so no solution.

Lab controls

Step speed1200 ms per step

Left or Down one step slower, Right or Up one step faster, Page Down 600 ms, Page Up 2400 ms, Home 600 ms, End 2400 ms

Step0

Left and Right move by 1, Page Up and Page Down move by 5, Home goes to step 0, End goes to the last step

Frame 1 of 18: Write the augmented matrixWrite the 3 equations as one table. The first 3 columns hold the coefficients and the last column holds the right-hand side.

Keyboard: Space plays or pauses, Left and Right step, Home goes to the first frame, End goes to the last frame.

Text description of this lab

A three-by-four augmented table holds one number per cell. A gold dashed outline marks the row being rewritten and a russet outline marks the pivot, and each frame applies one row operation. Three pivots in the first system give one point. The same coefficients then return with a different right-hand side: two pivots leave z free and the answers form a line, while the last change makes a zero row read 0 = 1, so there is no solution.

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Caption status: schematic. Every lab declares one of published, re-simulated, schematic, synthetic or interpolated.