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# Equivalence theorem for nonsingular matrices: the rows of A are linearly independent.

**Theorem:** An  	imes $n \times n$ matrix $A$ is nonsingular if and only if Theiff the rows of $A$ are linearly independent. No nontrivial linear combination of rows gives the zero vector. For $n$ rows in $\mathbb{R}^n$, independence implies they form a basis, equivalent to nonsingularity.

# Parents

* Nonsingular matrices and equivalences