Monthly Archives: July 2013

Exercise 2.6.11. Consider the vector space of functions in for which . From the previous exercise we can express any such function as where and are basis vectors for W. Suppose at we have and . Find and such that … Continue reading →

Exercise 2.6.10. Consider the vector space of functions in for which . Find two functions that can serve as basic vectors for the space. Answer: For a function to be in the space its second derivative with respect to must … Continue reading →

Exercise 2.6.9. Considering taking a polynomial from , the space of cubic polynomials in , and multiplying it by the polynomial to produce a polynomial in , the space of polynomials in of degree four. Describe a matrix representing this multiplication … Continue reading →

Exercise 2.6.8. If is the space of cubic polynomials in , what matrix would represent ? What are the nullspace and column space of this matrix? What polynomials would they represent? Answer: consists of all polynomials of the form . … Continue reading →