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$$ A \text{ is a Matrix in } \mathbb{R}^{n\times n} \text{ such that:} \left | a_{i,i} \right | > \sum_{\substack {j=1 \\j\neq i}}^{n} \left | a_{i,j} \right | \quad \text{ for all } i \in \left \{ {1..n} \right \} $$ Prove that A is invertible.

(By the way I'm looking for a solution that does not involve eigenvalues and determinants because we haven't studied them yet, we only studied linear maps and transformation matrices)


marked as duplicate by darij grinberg, user10354138, Theo Bendit, YuiTo Cheng, Community Jun 10 at 14:42

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