Gaussian Elimination: the algorithm hiding inside NumPy that I was doing by hand

Short summary

A backend engineer learning linear algebra discovers that Gaussian elimination—the algorithm they're solving by hand—is the same one running inside NumPy, optimized as LU decomposition. Linear algebra isn't background knowledge for ML; it's the fundamental substrate: backprop is the chain rule, attention is matrix multiplication, embeddings use inner products. Engineers who understand what's inside production libraries make better architectural decisions.

• •Hand-worked Gaussian elimination is the core algorithm inside NumPy, optimized as LU decomposition
• •Linear algebra is not background context for ML; it's the fundamental substrate of all deep learning systems
• •Understanding the math inside production libraries leads to better engineering decisions

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