Solution) Let A:(U,F)→ (V,F) with dim U = n and dim V = m be a linear map with rank(A) = k. Show that the
Question: Let \(A:\left( U,F \right)\to \left( V,F \right)\) with dim U = n and dim V = m be a linear map with rank(A) = k. Show that there is exist bases \(\left( {{u}_{i}} \right)_{i=1}^{n},\left( {{v}_{j}} \right)_{j=1}^{m}\) of U and V respectively such that with respect to those bases A is represented by the block diagonal matrix
\[A=\left[ \begin{matrix} I & 0 \\ 0 & 0 \\ \end{matrix} \right]\]What are the dimensions of the different blocks?
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Type of Deliverable: Word Document
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