Monthly Archives: September 2013

Exercise 2.6.21. Consider the transformation from to that takes into . What is the axis of rotation for the transformation? What is the angle of rotation? Answer: We can approach this problem in at least two ways. The first way … Continue reading →

Exercise 2.6.20. A nonlinear transformation from a vector space to a vector space is invertible a) if for any in there exists some in such that and b) if and are in then implies that . Describe which of the … Continue reading →

Exercise 2.6.19. Let be the vector space consisting of all cubic polynomials of the form and let be the subset of consisting of only those cubic polynomials for which . Show that is a subspace of and find a set … Continue reading →

Exercise 2.6.18. Given a vector in find a matrix that produces a corresponding vector in in which all entries are shifted right one place. Find a second matrix that takes a  vector in and produces the vector in in which … Continue reading →

Exercise 2.6.17. Find a matrix corresponding to the linear transformation of cyclically permuting vectors in such that applied to produces . Determine the effect of and and explain why . Answer: We can construct by considering its effect on the … Continue reading →

Exercise 2.6.16. Consider the space of 2 by 2 matrices. Any such matrix can be represented as the linear combination of the matrices that serve as a basis for the space. Find a matrix corresponding to the linear transformation of … Continue reading →

In doing the answers to exercise 2.6.14 in Gilbert Strang’s Linear Algebra and Its Applications, Third Edition I noticed one of the downsides of the book: While Strang’s focus on practical applications is usually welcome, sometimes in his desire to … Continue reading →