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

Put content here**Theorem:** An  	imes n$ matrix $ is nonsingular if and only if 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