Let A be a m x n matrix of rank r. 1. Prove that there exist...
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Let A be a m x n matrix of rank r. 1. Prove that there exist matrices M and E, of size m x r and r x n respectively, such that M has linearly independent columns and E has linearly independent rows, and A = ME. 2. Prove that, under the conditions above, M has a left inverse and E has a right inverse. Let A be a m x n matrix of rank r. 1. Prove that there exist matrices M and E, of size m x r and r x n respectively, such that M has linearly independent columns and E has linearly independent rows, and A = ME. 2. Prove that, under the conditions above, M has a left inverse and E has a right inverse.
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