## Linear Algebra and Its Applications, Exercise 3.4.22

Exercise 3.4.22. Given an arbitrary function find the coefficient that minimizes the quantity (Use the method of setting the derivative to zero.) How does this value of compare with the Fourier coefficient ? What is if ? Answer: We are … Continue reading

## Linear Algebra and Its Applications, Exercise 3.4.21

Exercise 3.4.21. Given the function on the interval , what is the closest function to ? What is the closest line to ? Answer: To find the closest function to the function we first project onto the function on the … Continue reading

## Linear Algebra and Its Applications, Exercise 3.4.20

Exercise 3.4.20. Given the vector what is the length ? Given the function for what is the length of the function over the interval? Given the function for what is the inner product of and ? Answer: We have so … Continue reading

## Linear Algebra and Its Applications, Exercise 3.4.19

Exercise 3.4.19. When doing Gram-Schmidt orthogonalization, an alternative approach to computing (equation 7 on page 173) is to instead compute in two separate steps: Show that the second method is equivalent to the first. Answer: We substitute the expression for … Continue reading

## Linear Algebra and Its Applications, Exercise 3.4.18

Exercise 3.4.18. If is the projection matrix onto the column space of the matrix and , what is a simple formula for ? Answer: The projection matrix onto the column space of can be calculated as . Since the columns … Continue reading