Definition of inverse that a square matrix
Please prove directly from definition of inverse that a square matrix A is invertible if and only if it has full rank, without talking about the connection between determinants and inverses.
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Suggest the following all-integer linear program: Max 5x1 +8x2 s.t. 6x1 + 5x2 <30, 9x1+4x2<36,1x1+2x2<10, x1,x2 > 0 and integer.
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