Given a matrix $A\in M_{n\times n}(\mathbb{R})$, show that if the vectors $v_1, \dots, v_m$ are linearly independent and $Av_1, \dots, Av_m$ also are linearly independent, then $A$ must be invertible.
2026-04-04 08:42:32.1775292152
Matrix product with linearly independent vectors
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