Linear system
A linear system asks for x satisfying Ax = b. It can have no solution, one solution, or infinitely many.
Definition
A linear system asks for x satisfying Ax = b. It can have no solution, one solution, or infinitely many.
Intuition
A solution exists exactly when b lies in the column space of A.
Worked example
x + y = 3 and x − y = 1 give x = 2 and y = 1.
The math
If is one solution, all solutions are with .
In machine learning
Use a factorization-based solver for a system; explicitly computing an inverse is usually unnecessary.
Go deeper
Sources
More in Linear algebra
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