Monthly Archives: August 2013

Exercise 2.6.15. Suppose that is a linear transformation from to itself, or more generally from any vector space to itself. Show that is also a linear transformation. Answer: If is a linear transformation from some vector space to itself then … Continue reading →

Exercise 2.6.14. Suppose that , , and are linear transformations, with taking vectors from to , taking vectors from to , and  taking vectors from to . Consider the product of these transformations. It starts with a vector in and … Continue reading →

Exercise 2.6.13. Suppose that is a linear transformation from the – plane to itself. If a transformation exists such that show that is also linear. Also show that if is the matrix representing then the matrix representing must be . … Continue reading →

Exercise 2.6.12. If is the reflection matrix in the – plane, show that using the trigonometric identity ( for short). Answer: We have so that Since this can be simplified to NOTE: This continues a series of posts containing worked … Continue reading →