Reading: Text: Sections 7.2 and 6.1 (through p. 308)
Assigned Problems:Section 7.2 (See hints and notes below): 1(a,c,f), 2, 6(a,b,c), 9, 13, 24(b,c), 25(b), 26(c)
Hint for 7.2.1(c): Note that the second matrix in Eq. (4.31) of the textbook maps e1 to u1 and e2 to u2 in Figure 4.2 on p. 202. Conclude that the corresponding linear transformation is a reflection through the line obtained by rotating the x-axis counterclockwise through an angle θ/2. What is tan(θ/2) for the line y = 2x? Use it to figure out what cos θ and sin θ are. Beware that the answer to 7.2.1(c-ii) in the Students' Solution Manual is incorrect. Thanks to Cassandra Chanthamontry for noticing this.
Hint for 7.2.1(f): Find an orthonormal basis of the line y = 2x, regarded as a subspace of ℝ2, and use Theorem 4.32.
Note for 7.2.6: There is an error in the Students' Solution Manual, discovered by Jacob Boerjan. There is a weird shift in the solution numbering. Solution (a) answers the unlabeled problem to draw the given parallelogram. Solution (c) answers Question (b), Solution (g) answers Question (f).
Note for 7.2.26: You may use a graphing calculator or your favorite software, such as Matlab, Mathematica, Maple, or the link "all your mathematica needs" on the main class web page to compute T-1 and B = T-1AS to check your answer. Otherwise, computing T-1 might be a harrowing experience.
Section 6.1: 1, 3, 5(a), 8
Note for 6.1.8(b): "Answer Exercise 6.1.8..." in the textbook should be replaced with "Answer Part (a)..." You may also use your graphing calculator or some Math software to compute K-1 with spring stiffnesses c1, c2, and c3 kept as variables, but you do not have to. It is computable by hand, too.
Challenge Problems (for digging deeper into Linear Algebra -- not to be turned in):
Section 7.2: 28
Section 6.1: 5(b), 6, 10
Last modified: (2018-11-23 16:07:45 CST)