Reference request: matricial representation of conics (and quadrics too)

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Can anybody please provide me some references where to read the complete passages / proofs about how and why the matricial representation of conics and quadrics are useful and they work?

I mean, the theory is rather simple. We can classify conics by looking at the three invariants. Where can I learn how all of this is born?

Thank you!

P.s. Before anyone says it: wikipedia's references are not useful/enough.