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Exercise:
Let Ain M_mtimes nK bin K^m. The following statements are equivalent: abcliste abc textrankA|btextrankA. abc The system of s Axb has a solution. abcliste

Solution:
Proof. Write A pmatrix vdots & & vdots v_ & hdots & v_n vdots & & vdots pmatrix. We have: a&iff textcol-rankA|btextcol-rankAiff textSpv_...v_nbtextSpv_...v_n &iff bin textSpv_...v_niff bextCol SAiff textSolAbneq varnothing
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Exercise:
Let Ain M_mtimes nK bin K^m. The following statements are equivalent: abcliste abc textrankA|btextrankA. abc The system of s Axb has a solution. abcliste

Solution:
Proof. Write A pmatrix vdots & & vdots v_ & hdots & v_n vdots & & vdots pmatrix. We have: a&iff textcol-rankA|btextcol-rankAiff textSpv_...v_nbtextSpv_...v_n &iff bin textSpv_...v_niff bextCol SAiff textSolAbneq varnothing
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eth, hs22, lineare algebra, matrices, proof, rank
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ENG (English)
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