Math 528

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Unofficial errata

• HW due 10/30: 6.2.4, 6.2.8, 6.2.9, 6.2.14, 6.3.2, 6.3.11
• HW due 10/23: 4.2.1, 4.2.6, 4.2.9aceg (for e, use the linearity on both sides of your rule to simplify the proof), 4.4.1, 4.4.3, 4.4.5
• HW due 10/16: 3.3.5, 3.3.6, 3.3.7, 3.4.2, 3.4.4, 3.4.10
  HW 5 selected solutions
• HW due 10/9: 3.1.5, 3.1.8, 3.1.13, 3.2.2, 3.2.7, 3.2.9, and the following:
  • A. Let \(V = F[x]\), and let \(D, X, I \in L(V, V)\) be defined as follows: \(D\) is differentiation, \(X(f) = xf\) (multiplication by \(x\)), and \(I\) is the identity. Compute \(\ker(XD - I)\). Make sure to prove your answer!
    HW 4 selected solutions
• HW due 10/2: 2.3.7, 2.4.6, 2.6.6 (for b, give equations for the \(x_i\)), and the following:
  • A. Suppose \(V\) is a vector space and \(L = (\alpha_1, \ldots, \alpha_n)\) is a list of vectors spanning \(V\). Given an algorithm for finding a sublist of \(L\) which is a basis for \(V\). Prove that your algorithm works.
  • B. Let \(F = \mathbb{Z}/2\mathbb{Z}\) and \(V = F^n\). How many ordered bases does \(V\) have?
  
  HW 3 selected solutions
• No HW due 9/25. For practice, do 2.3.4, 2.3.5, 2.3.6, 2.3.7, 2.3.10, 2.3.14
• HW due 9/18: 1.6.6, 1.6.9, 2.1.4, 2.1.6, 2.2.5 (remember \(F\) can be a finite field for your justifications), 2.2.7, 2.2.8
  HW 2 selected solutions
• HW due 9/11: 1.2.4, 1.2.6, 1.3.1, 1.3.4
  HW 1 selected solutions