It is proved that the mxn matrix A with rank r (r > 0) can be decomposed into the sum of R mxn matrices with rank 1 Is m x n matrix Detailed process

Use elementary transformation to construct decomposition, as shown in the figure. The economic mathematics team will help you solve it. Please evaluate it in time. Thank you!

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1. Let a be an sxn matrix and B be an mxn matrix composed of the first m rows of A. It is proved that if the rank of the row vector group of a is r, then R (b) > = R + m-s
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