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winwinphyo
winwinphyo
05.05.2020 • 
Mathematics

G 4. (5 points) If A is an m × n matrix, prove that the null space of AT and the column space of A are orthogonal complements in R m. For example, show that N(AT ) = (C(A))⊥ . (Note that C(A) = N(AT ) ⊥ is also true). Note: Because of Theorem 4.8.6 (c) See Text Page 253, that is (W⊥) ⊥ = W, once we have N(A) = (R(A))⊥ , then R(A) = (N(A))⊥ will also follows. Similarly, once we have N(AT ) = (C(A))⊥ , then C(A) = N(AT ) ⊥ will also follows. Note: The results obtained in Problem 3 and 4 are also refered to as Fundamental Theorem of Linear Algebra, this shows its important in the subject

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