Linear Algebra
Transforming the plane…
Initializing Sorting Algorithms...
Sorting
Trees
Graphs
Preparing interactive visualizations...
Linear Algebra
Transforming the plane…
Row-reduce [A | I] until the left side is I, and the right side is A⁻¹. Then watch A⁻¹ do its job: put the plane back exactly where A found it.
2×2: A = [(4, 2), (3, 2)]. Write it next to the identity, [A | I], and row-reduce until the left half is I. Every operation is applied to the whole row, so the right half records them all.
| R₁ | 4 | 2 | 1 | 0 |
| R₂ | 3 | 2 | 0 | 1 |
det A = 2. A⁻¹ appears in the right half once the left half is I.