Question: Suppose is with rank . Prove there exists matrix such that . I am kind of stuck on this. Any hints on which properties or theorems on rank of matrices that I should appeal to? Thanks!
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Originally Posted by Last_Singularity Question: Suppose is with rank . Prove there exists matrix such that . I am kind of stuck on this. Any hints on which properties or theorems on rank of matrices that I should appeal to? Thanks! let be the standard basis for and let be the linear map with this map is onto because so for any there exists such that now define by see that is a linear map and let we have because
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