Labs / Mathematics
Solving Linear Systems
A system of equations and its augmented matrix sit side by side. Press Step (or Auto-run) to apply one elementary row operation at a time — swapping, scaling, and subtracting rows — until the matrix collapses to reduced row-echelon form and the answer just falls out. For a 2×2 system, each equation is a line, and the solution is exactly where the two lines cross.
step 0 / 0op —solution —cursor —
What to try
- In the "No solution" system, watch the matrix. What does the row that becomes 0 = a nonzero number tell you about the two lines?
- For "Infinite" solutions, why do the two lines land exactly on top of each other, and how does the matrix reveal that a variable is free?
- Switch between 2×2 and 3×3 — does adding a third equation always pin down a single point, or can it still fail?
- Hit Randomize a few times. Can you predict from the equations alone whether you'll get one answer, none, or infinitely many before you step through?
- Does the order in which you clear the columns change the final answer, even though the intermediate matrices look different?