Homework 3

All questions are from Penney, Linear Algebra, 4th edition. For each question that's more than just a calculation, justify your reasoning in complete sentences. Please staple your work and label each problem clearly. Each problem is worth 5 points.

• True or False questions 1.22 (p. 62), 1.33 and 1.34 (p. 85).
• Exercises 1.65(b) and (f), 1.69, 1.79, 1.86 (p. 63-68).
• Write the function g(x) = x³ as a lineasr combination of the following functions: f₁(x) = 4x³ - 3x, f₂(x) = 2x² - 1, f₃(x) = x - 1, f₄(x) = 1.
• Pick another exercise from section 1.3 that looks interesting, and do it.