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Monthly Archives: October 2016
Linear Algebra and Its Applications, Exercise 3.3.15
Exercise 3.3.15. Suppose is a projection matrix that projects vectors onto a line in the – plane. Describe the effect of the reflection matrix geometrically. Why does ? (Give both a geometric and algebraic explanation.) Answer: When applied to a … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.14
Exercise 3.3.14. Find the projection matrix onto the plane spanned by the vectors and . Find a nonzero vector that projects to zero. Answer: The plane in question is the column space of the matrix The projection matrix . We have … Continue reading
Posted in linear algebra
Tagged column space, left nullspace, plane, projection matrix
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Linear Algebra and Its Applications, Exercise 3.3.13
Exercise 3.3.13. Using least squares, find the line that is the best fit to the following measurements: at at at at Also, given the matrix find the projection of onto the column space . Answer: Assuming that the line in … Continue reading
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
Posted in linear algebra
Tagged basis, column space, left nullspace, orthogonal complement, projection matrix
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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