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Monthly Archives: September 2016
Linear Algebra and Its Applications, Exercise 3.3.10
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
Linear Algebra and Its Applications, Exercise 3.3.9
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
Linear Algebra and Its Applications, Exercise 3.3.8
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
Linear Algebra and Its Applications, Exercise 3.3.7
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