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Tag Archives: orthogonal complements
Linear Algebra and Its Applications, Exercise 3.1.22
Exercise 3.1.22. Consider the equation and the subspace of containing all vectors that satisfy it. Find a basis for , the orthogonal complement of . Answer: is the nullspace of the linear system where Since is the nullspace of its … Continue reading
Linear Algebra and Its Applications, Exercise 3.1.20
Exercise 3.1.20. Suppose is a subspace of . Show that . What does this mean? Answer: We first consider the case where ; in other words, contains only the zero vector. From exercise 3.1.18 we know that . The only … Continue reading