ma253, Fall2007— Problem Set LastThis is abigassignment. The theory of eigenvalues and eigenvectors iscritical and will be the main focus of the final exam. In order find eigenval-ues, you need to understand determinants at least a little bit. This assign-ment tries to get you to really think about both things. Let’s make it due onthe last day of classes,Friday, December 7.1.Problems from the textbook:a. Section6.1, problems *26,28, *30, *32, *44.b. Section6.2, problems *4, *6(do these two by hand), *14, *16, *18,*30,50(the last one is very hard).c. Section7.1, problems1–5, *6, *8,15–19,33, *36.d. Section7.2, problems1–7, *8, *10, *12,15, *16, *28, *33, *38.e. Section7.3, problems1–5, *6,7–9, *10, *14, *18,35,36,48.f. Section7.4, problems1–8, *10, *12, *18.*2.Supposevis an eigenvector of an invertiblen×nmatrixA, correspond-ing to an eigenvalueλ. LetIbe the identity matrix.a. Isvan eigenvector ofA3? If so, what is the eigenvalue?b. Isvan eigenvector ofA-1? If so, what is the eigenvalue?