Suppose $A$ is an nxn matrix, then if we have $|Ah|\geq c|h|$ for some positive $c$, can we say $A$ is invertible? Notice that $|.|$ is the Euclidean norm!
2026-04-06 05:52:01.1775454721
Prove the $\ Det A$ is nonzero
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A matrix is invertible if it has trivial kernel. If for every nonzero $h$ we have $|Ah|\geq c|h|$, in particular $Ah\neq 0$, so $A$ has trivial kernel.