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Monthly Archives: November 2016
Linear Algebra and Its Applications, Exercise 3.3.19
Exercise 3.3.19. Given a matrix , the matrix projects onto the column space of . Find the matrix that projects onto the row space of . Answer: The row space of is the column space of . We can then … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.18
Exercise 3.3.18. Suppose we have the following measurements of : and want to fit a plane of the form . a) Write a system of 4 equations in 3 unknowns representing the problem. (The system may not have a solution.) b) Write … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.17
Exercise 3.3.17. Find the projection matrix that projects vectors in onto the line . Answer: The vector is a basis for the subspace being projected onto, which is thus the column space of Using the formula we have so that and … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.16
Exercise 3.3.16. Suppose is a vector with unit length. Show that the matrix (with rank 1) is a projection matrix. Answer: We have But since has unit length we have so that We also have Since and the rank1 matrix is … Continue reading