1. (25%) Let n n T : be a linear transformation with R → R T x Ax v v ( ) = , where A is an n× n matrix. Write down as many as possible equivalent statements of “ A is invertible”, and sketch the proof.
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1. (25%) Let n n T : be a linear transformation with R → R T x Ax v v ( ) = , where A is an n× n matrix. Write down as many as possible equivalent statements of “ A is invertible”, and sketch the proof.