# Monthly Archives: December 2016

## Linear Algebra and Its Applications, Exercise 3.3.24

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

## Linear Algebra and Its Applications, Exercise 3.3.23

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

## Linear Algebra and Its Applications, Exercise 3.3.22

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

## Linear Algebra and Its Applications, Exercise 3.3.21

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

## Linear Algebra and Its Applications, Exercise 3.3.20

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