Monthly Archives: October 2016

Linear Algebra and Its Applications, Exercise 3.3.15

Posted on October 29, 2016 by hecker

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 →

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Linear Algebra and Its Applications, Exercise 3.3.14

Posted on October 22, 2016 by hecker

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 →

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Linear Algebra and Its Applications, Exercise 3.3.13

Posted on October 15, 2016 by hecker

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 →

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Linear Algebra and Its Applications, Exercise 3.3.12

Posted on October 8, 2016 by hecker

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

Posted on October 1, 2016 by hecker

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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