Monthly Archives: December 2016

Linear Algebra and Its Applications, Exercise 3.3.24

Posted on December 31, 2016 by hecker

Exercise 3.3.24. Given the measurements at use least squares to find the line of best fit. Answer: This corresponds to a system of the form as follows: To find the least squares solution we multiply both sides by to create a system … Continue reading →

Posted in linear algebra | Tagged | Leave a comment

Linear Algebra and Its Applications, Exercise 3.3.23

Posted on December 24, 2016 by hecker

Exercise 3.3.23. Given measurements show that the best least squares fit to the horizontal line is given by Answer: This corresponds to the system where is an by 1 matrix with all entries equal to 1 and . To find the … Continue reading →

Posted in linear algebra | Tagged , | Leave a comment

Linear Algebra and Its Applications, Exercise 3.3.22

Posted on December 17, 2016 by hecker

Exercise 3.3.22. Given measurements of at use least squares to find the line of best fit of the form . Answer: This corresponds to a system as follows: To find the least squares solution we form the system . We have and … Continue reading →

Posted in linear algebra | Tagged | Leave a comment

Linear Algebra and Its Applications, Exercise 3.3.21

Posted on December 10, 2016 by hecker

Exercise 3.3.21. Given three vectors , , and , and the two lines through the origin and and through in the direction of , we want to find scalar values and such that the distance between the points and is … Continue reading →

Posted in linear algebra | Tagged | Leave a comment

Linear Algebra and Its Applications, Exercise 3.3.20

Posted on December 3, 2016 by hecker

Exercise 3.3.20. Given the matrix that projects onto the row space of , find the matrix that projects onto the nullspace of . Answer: The null space of is orthogonal to the row space of . The two spaces are orthogonal complements, with … Continue reading →

Posted in linear algebra | Tagged , , | Leave a comment