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Homework 6
- Section 6.1 The Scalar Product in \(\mathbb{R}^n\)
- Read Section 6.1. Do the True/False questions (pp. 325-326). Do Problems 6.1(a)(c), 6.2(a)(c)(e).
- Homework: 6.1(b), 6.2(d), 6.3, 6.5, 6.6, 6.7, 6.11 (Use Theorem 6.2.), 6.15
- Hand In: 6.7*, 6.11
- 6.7*. Complete Problem 6.7 on Page 327, but with the basis \[\mathcal{B}^{\prime\prime} = \left\{\frac{1}{\sqrt{2}}\left[\matrix{1\cr 0\cr 1\cr}\right],\frac{1}{\sqrt{3}}\left[\matrix{-1\cr 1\cr 1\cr}\right], \frac{1}{\sqrt{6}}\left[\matrix{1\cr 2\cr -1\cr}\right]\right\}.\]
- 6.11. Complete Problem 6.11 on Page 327 as stated in the text. (Use Theorem 6.2.)
- Read Section 6.2. Do the True/False questions (p. 338). Do Problems 6.17(a), 6.20(a)(c).
- Homework: 6.20(d), 6.21, 6.22 (use the Gram-Schmidt process), 6.24, 6.25, 6.26, 6.27(a)(b), 6.29, 6.36
- Hand In: 6.20(d)*, 6.22(b)* (use the Gram-Schmidt process), 6.25, 6.27(b)*
- 6.20(d)*. Complete Problem 6.20(d) on Page 339, but with the ordered set of vectors \[\{[1,1,1,-1]^t,[1,0,1,0]^t,[1,-1,1,-1]^t\}.\]
- 6.22(b)*. Complete Problem 6.22(b) on Page 339, but where A is the matrix \[A=\left[\matrix{1&1&1\cr -1&0&1\cr 1&-1&1\cr}\right].\] (Use the Gram-Schmidt process)
- 6.25. Complete Problem 6.25 on Page 339 as stated in the text.
- 6.27(b)*. Complete Problem 6.27(b) on Page 339, but with the set \(S=\{[-1,2,1,-1]^t,[2,4,-1,0]^t\}.\)