UNIT B.3 — MATHEMATICS

Linear algebra: solving systems

BRIDGE · EE Foundations Bridge · ~10 min

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A system of linear equations is several unknowns bound by several conditions: x + y = 6 and x − y = 2 pin down x = 4, y = 2. Linear algebra packages such systems into matrices — grids of coefficients — and solves them mechanically, whether there are 2 unknowns or 2 million.

Circuit analysis is the immediate payoff: applying KVL to a circuit with three loops (Unit B.1) yields three equations in three unknown currents. Matrix methods solve them in one sweep — this is precisely what circuit simulators like SPICE do under the hood, thousands of times per second.

The same machinery drives power-flow studies on the grid, 3-phase network analysis, control systems, and machine learning. It is the single most reusable branch of math in engineering.

Go deeper: Gilbert Strang's Linear Algebra — the most celebrated math course MIT has ever put online. Semester 1 of the Go Deeper pathway.

System
n equations · n unknowns
Matrix
The coefficient grid
Circuit use
Mesh/nodal analysis
Knowledge check

Quiz — 3 questions

1. If x + y = 10 and x − y = 4, then x =

2. A circuit with 4 independent loops analyzed by KVL produces:

3. Circuit simulators like SPICE fundamentally work by:

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