subject
Mathematics, 05.05.2020 02:34 charlotte67

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

ansver
Answers: 3

Another question on Mathematics

question
Mathematics, 21.06.2019 15:30
Franco wants to double the volume of the cone. what should he do?
Answers: 2
question
Mathematics, 21.06.2019 15:30
Answer question above and explain each step : )
Answers: 3
question
Mathematics, 22.06.2019 04:30
Acone with radius 5 cm and height 12 cm how many cm ?
Answers: 1
question
Mathematics, 22.06.2019 07:00
How do you find the angles inside a triangle with one extirer angle
Answers: 2
You know the right answer?
G 4. (5 points) If A is an m × n matrix, prove that the null space of AT and the column space of A a...
Questions
question
Mathematics, 24.02.2021 05:40
question
Physics, 24.02.2021 05:40
question
Mathematics, 24.02.2021 05:40
question
Spanish, 24.02.2021 05:40
question
Mathematics, 24.02.2021 05:40