Homogeneous system AX = 0 (Square case: zero determinant ⇔ nontrivial nullspace; always trivial if)

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Square case: zero determinant ⇔ nontrivial nullspace; always trivial if A invertible.

What each symbol means

SymbolWhat it stands for
XUnknown column vector

When to use this

For n×n equivalence with |A|=0; general case use rank(A)<n.