proposition 7.111 Jacobi's formula, cofactor form

Rests on

• depends_on equation 5.19 eq:lin-leibniz-det ¶
• depends_on proposition 7.31 Chain rule ¶
  • depends_on definition 7.13 Composite function ¶
    • depends_on definition 7.9 Real function ¶
      • depends_on definition 3.43 Map ¶
        • depends_on definition 3.24 Quantifiers ¶
        • depends_on definition 3.28 Set ¶
  • depends_on proposition 7.27 Differentiable implies continuous ¶
    • depends_on definition 7.20 Continuity at a point ¶
      • depends_on definition 7.16 Limit ¶
        • depends_on definition 7.2 Absolute value ¶
        • depends_on definition 7.9 Real function ¶ ↺
      • depends_on equation 7.7 eq:ana-limit-left ¶
      • depends_on equation 7.5 eq:ana-limit-right ¶
    • depends_on definition 7.26 Derivative of a function at a point ¶
      • depends_on definition 7.16 Limit ¶ ↺
      • depends_on definition 7.9 Real function ¶ ↺
    • depends_on proposition 7.6 Algebra of limits ¶
      • depends_on definition 7.4 Convergence ¶
        • depends_on definition 7.2 Absolute value ¶ ↺
      • depends_on proposition 7.3 Triangle inequality ¶
        • depends_on definition 7.2 Absolute value ¶ ↺
        • proves proof ch:05-real-analysis@proof-1 ¶
      • proves proof ch:05-real-analysis@proof-3 ¶
    • proves proof ch:05-real-analysis@proof-11 ¶
  • depends_on proposition 7.6 Algebra of limits ¶ ↺
  • proves proof ch:05-real-analysis@proof-15 ¶
• depends_on proposition 7.30 Leibniz rule ¶
  • depends_on definition 7.12 Product of functions ¶
    • depends_on definition 7.9 Real function ¶ ↺
  • depends_on equation 7.14 eq:ana-derivh ¶
  • depends_on proposition 7.27 Differentiable implies continuous ¶ ↺
  • depends_on proposition 7.6 Algebra of limits ¶ ↺
  • proves proof ch:05-real-analysis@proof-14 ¶
• depends_on proposition 5.2 Jacobi's formula, column form ¶
  • depends_on equation 5.19 eq:lin-leibniz-det ¶ ↺
  • depends_on proposition 7.30 Leibniz rule ¶ ↺
  • depends_on proposition 5.49 Injective, surjective, invertible ¶
    • depends_on definition 5.39 Kernel, image, nullity, rank ¶
      • depends_on definition 5.37 Linear transformation ¶
        • depends_on definition 4.33 Vector space ¶
      • depends_on definition 5.7 Vector subspace ¶
        • depends_on definition 5.5 Linear combination ¶
      • proves proof ch:03-linear-algebra-representations@proof-12 ¶
    • depends_on proposition 5.48 Existence, uniqueness, and linearity of the inverse ¶
      • depends_on definition 5.47 Inverse of a linear transformation ¶
        • depends_on definition 5.37 Linear transformation ¶ ↺
      • depends_on definition 5.37 Linear transformation ¶ ↺
      • proves proof ch:03-linear-algebra-representations@proof-17 ¶
    • depends_on theorem 5.40 Rank–nullity ¶
      • depends_on definition 5.15 Basis ¶
        • depends_on definition 5.12 Subspace generated by a set of vectors ¶
        • depends_on definition 5.14 Linear independence ¶
      • depends_on definition 5.39 Kernel, image, nullity, rank ¶ ↺
      • depends_on lemma 5.38 Exchange and completion ¶
        • depends_on definition 5.15 Basis ¶ ↺
        • depends_on definition 5.12 Subspace generated by a set of vectors ¶ ↺
        • depends_on definition 5.14 Linear independence ¶ ↺
        • proves proof ch:03-linear-algebra-representations@proof-11 ¶
      • proves proof ch:03-linear-algebra-representations@proof-13 ¶
    • proves proof ch:03-linear-algebra-representations@proof-18 ¶
  • proves proof ch:03-linear-algebra-representations@proof-1 ¶
• proves proof ch:05-real-analysis@proof-69 ¶

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