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Homework 4
- Section 2.1 The Test for Linear Independence
- Read Section 2.1. Do the True/False questions (p. 104). Do Problems 2.1(a)(d)(g)(j). WeBWorK reading question due September 13 @ 9:50 am.
- Homework: 2.1(b)(e)(f)(k), 2.3(a)(c)(d)(f), 2.5, 2.6, 2.9(a)(c), 2.11, 2.13, 2.16(a)(c)(e), 2.17(a)(c)(d)(f), 2.19
- Hand In: 2.1(k)*, 2.3(f)*, 2.9(c)*, 2.17(d)*
- 2.1(k)*. Complete Problem 2.1(k) on Page 105, but with the vectors \[\left[\matrix{3\cr 2\cr 4\cr 5\cr}\right], \left[\matrix{-4\cr -3\cr -5\cr -6\cr}\right], \left[\matrix{6\cr 3\cr 9\cr 12\cr}\right]\]
- 2.3(f)*. Complete Problem 2.3(f) on Pages 105-106, but with the matrix \[\left[\matrix{3&6&2&-7\cr 2&4&0&8\cr -1&-2&-1&-2\cr 2&4&-3&8\cr}\right]\]
- 2.9(c)*. Complete Problem 2.9(c) on Page 107, but with \(Y_1=X_1+3X_2-X_3, Y_2=X_1-X_2\) and \(Y_3=5X_2\).
- 2.17(d)*. (Edited due to online version of text showing a random matrix instead of sets of functions:) Show that the set \(\{x^3,x^4,x^5\}\) (of infinitely differentiable functions) is linearly independent using the test for linear independence.
- WeBWorK assignment for Section 2.1 due September 22 @ 11 pm
- Read Section 2.2. Do the True/False questions (p. 118). Do Problems 2.20, 2.22, 2.24(a). WeBWorK reading question due September 18 @ 9:50 am.
- Homework: 2.24(b)(c), 2.25, 2.26, 2.27, 2.29, 2.30, 2.33, 2.35, 2.36, 2.38, 2.41, 2.43, 2.45
- Hand In: 2.24(c)*, 2.27(c)*, 2.30(c)*, 2.38*
- 2.24(c)*. Complete Problem 2.24(c) on Page 119, but with \[\mathcal{W}=\{[a+b+2c,2a+b+3c,a+2b+c]^t\ \vert\ a, b, c \in \mathbb{R}\}.\]
- 2.27(c)*. Complete Problem 2.27(c) on Page 119, but where A is lower triangular (and \(3\times 3\)).
- 2.30(c)*. Complete Problem 2.30(c) on Page 120, but with the matrix \[\left[\matrix{1&-5&2&3\cr 2&-10&4&6\cr 4&-20&8&12\cr}\right]\]
- 2.38*. Complete Problem 2.38 on Page 121, but with \(X = 2A-3B\) and \(Y = 3A+5B.\)