Tag Archives: orthogonal complement

Linear Algebra and Its Applications, Exercise 3.3.12

Exercise 3.3.12.¬†Given the subspace spanned by the two vectors and find the following: a) a set of basis vectors for b) the matrix that projects onto c) the vector in that has the minimum distance to the vector in Answer: … Continue reading

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Linear Algebra and Its Applications, Exercise 3.3.11

Exercise 3.3.11. Suppose that is a subspace with orthogonal complement , with¬† a projection matrix onto and a projection matrix onto . What are and ? Also, show that is its own inverse. Answer: Given any vector we have where … Continue reading

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Linear Algebra and Its Applications, Exercise 3.1.18

Exercise 3.1.18. Suppose that is the subspace of containing only the origin. What is the orthogonal complement of ()? What is if is the subspace of spanned by the vector ? Answer: Every vector is orthogonal to the zero vector. … Continue reading

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Linear Algebra and Its Applications, Exercise 3.1.9

Exercise 3.1.9. For the plane in spanned by the vectors and find the orthogonal complement (i.e., the line in perpendicular to the plane). Note that this can be done by solving the system where the two vectors are the rows … Continue reading

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