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One way is to start with empty matrix. Add the first column. Then loop, each time adding the next column, and checking if the rank of this matrix has increased from before, if so, keep it, else skip over to the next column. Keep doing this until you reach the last column in the original matrix, or have collected m columns, where m is the rank of the original ...


If RowReduce won't help, then perhaps I don't know what you're looking for. Here's my understanding of the question in which I use RowReduce to get the answer. Example A random matrix: SeedRandom[1]; mat = RandomSample[#~Join~Accumulate@RandomSample[#, 2] &@ RandomInteger[{-5, 5}, {35, 37}]]; MatrixRank[mat] (* 35 *) We can use the ...


Since nobody has posted a "messy" solution yet, let me: if the matrices are in one list alist = {a1,a2,...,an} and the rhs' are in another, blist = {b1,b2,...,bn} then Clear[x]; vars = x[#] & /@ Range[n]; vars /. Solve[Dot[#1, vars] == #2 & @@@ Transpose[{alist, blist}], vars]

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