Monthly Archives: September 2016

Linear Algebra and Its Applications, Exercise 3.3.10

Posted on September 24, 2016 by hecker

Exercise 3.3.10. Given mutually orthogonal vectors , , and and the matrix with columns  and , what are and ? What is the projection of onto the plane formed by and ? Answer: We have where the zero entries are the result … Continue reading →

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Linear Algebra and Its Applications, Exercise 3.3.9

Posted on September 17, 2016 by hecker

Exercise 3.3.9. Suppose that is a matrix such that . a) Show that is a projection matrix. b) If then what is the subspace onto which projects? Answer: a) To show that is a projection matrix we must show that and also … Continue reading →

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Linear Algebra and Its Applications, Exercise 3.3.8

Posted on September 10, 2016 by hecker

Exercise 3.3.8. Suppose that is a projection matrix from onto a subspace with dimension . What is the column space of ? What is its rank? Answer: Suppose that is a arbitrary vector in . From the definition of we know … Continue reading →

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Linear Algebra and Its Applications, Exercise 3.3.7

Posted on September 3, 2016 by hecker

Exercise 3.3.7. Given the two vectors and find the projection matrix that projects onto the subspace spanned by and . Answer: The subspace spanned by  and is the column space where The projection matrix onto the subspace is then . We … Continue reading →

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