Math 110: Linear Algebra Practice Midterm #2

∗Note The theorems in sections 5.1 and 5.2 each have two versions, one stated in terms of linear operators, one in terms of matrices. The book states most of them in terms of linear operators, whilst in the lecture notes, they are mostly stated in terms of matrices. For example, compare Theorem 5.5 and its corollary in the book with Theorem 5 and its corollary in the lecture notes; also compare Theorem 5.6 in the book with the computation of the characteristic polynomial of a diagonalizable matrix done in lectures. In each case, one can derive one version from the other, by considering LA and [T ]β. In these solutions I’ll reference theorems in the book, but often I literally mean the matrix version of that theorem.