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https://texercises.com/exercise/rank-and-linear-equations-ii/
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Exercise:
Let Ain M_mtimes nK bin K^m. The following statements are equivalent: abcliste abc textrankA|btextrankAn. abc The system of s Axb has a unique solution. abcliste

Solution:
Proof. Write A pmatrix vdots & & vdots v_ & hdots & v_n vdots & & vdots pmatrix. We have: textrankAniff textdim Spv_...v_nniff v_...v_nquad textform a basis for Col SA to be completed exercise.
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Exercise:
Let Ain M_mtimes nK bin K^m. The following statements are equivalent: abcliste abc textrankA|btextrankAn. abc The system of s Axb has a unique solution. abcliste

Solution:
Proof. Write A pmatrix vdots & & vdots v_ & hdots & v_n vdots & & vdots pmatrix. We have: textrankAniff textdim Spv_...v_nniff v_...v_nquad textform a basis for Col SA to be completed exercise.
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eth, hs22, lineare algebra, matrices, proof, rank
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ENG (English)
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