# Tag Archives: least squares

## 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 3.3.13

Exercise 3.3.13. Using least squares, find the line that is the best fit to the following measurements: at at at at Also, given the matrix find the projection of onto the column space . Answer: Assuming that the line in … Continue reading

## Linear Algebra and Its Applications, Exercise 3.3.5

Exercise 3.3.5. Given the system with no solution, provide a graph of a straight line that minimizes and solve for the equation of the line. What is the result of projecting the vector onto the column space of ? Answer: … Continue reading

## Linear Algebra and Its Applications, Exercise 3.3.4

Exercise 3.3.4. Given expand the expression , compute its partial derivatives with respect to and , and set them to zero. Compare the resulting equations to to confirm that you obtain the same normal equations in both cases (i.e., using … Continue reading

Posted in linear algebra | | 2 Comments

## Linear Algebra and Its Applications, Exercise 3.3.3

Exercise 3.3.3. Given solve to find . Show that is orthogonal to every column in . Answer: We have or if is invertible. In this case we have so that We then have and The error vector is then The … Continue reading