Linear Algebra B — Inverses & Solving Systems
Part 2 of 2. The matrix inverse (and when it exists), and solving linear systems with Cramer's rule — systems as matrix equations.
Part 2 of 2. If a matrix is a machine, its inverse is the undo button — and that's exactly what solving a system of equations needs.
- 01 The inverse — undoing the machine ELI5: M⁻¹ reverses whatever M did, just like 1/x undoes ×x. It exists only when det ≠ 0 — a machine that flattened space (det = 0) destroyed information and…
- 02 Solving systems — Cramer's rule ELI5: a system like 2x + y = 8, x − y = 1 is secretly a matrix equation A·[x, y] = [8, 1]. Cramer's rule solves it with determinants alone: to get x, swap…
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