A printed version of this page has no headers, footers, menu bars or this message.
Homework 7
- Section 3.4 The LU Decomposition
- Read Section 3.4. Do Problems 3.104(a)(b), 3.105(a)(d).
- Homework: 3.105(d) (do NOT use any row interchanges or row multiples!), 3.108, 3.111, 3.112, 3.113, 3.114, 3.115
- Hand In: 3.105(d)* (do NOT use any row interchanges or row multiples!), 3.113*
- 3.105(d)*. Complete Problem 3.105(d) on Page 214, but with the matrix \[\left[\matrix{2&3&4\cr 1&2&2\cr 1&3&2\cr}\right]\]
- 3.113*. Complete Problem 3.113 on Page 215, but with \(R_1\) and \(R_2\) exchanged and \(R_3\) and \(R_4\) exchanged.
- Read Section 3.5. Do the True/False questions (p. 230). Do Problems 3.121(b), 3.123(b).
- Homework: 3.118, 3.120, 3.121(d), 3.122(a), 3.124 (actually check that M is given by the indicated formula), 3.125, 3.128 (only use the matrix A in those parts that refer to A), 3.130, 3.136
- Hand In: 3.121(d)*, 3.125(c)*, 3.128(h)* (note part (h) does not make use of the matrix A), 3.136*
- 3.121(d)*. Complete Problem 3.121(d) on Page 232, but with the basis \(\mathcal{B}=\{[1,1,2]^t, [-1,1,-1]^t,[2,1,-2]^t\}\).
- 3.125(c)*. Complete Problem 3.125(c) on Page 233, but with the matrix \[A=\left[\matrix{3&1&2\cr 4&6&5\cr}\right]\] and the basis \(\mathcal{B}=\{[1,1,2]^t, [-1,1,-1]^t,[2,1,-2]^t\}\).
- 3.128(h)*. Complete Problem 3.128(h) on Page 234, but with the linear transformation \(L\ :\ M(2,3)\to M(3,2)\), where \(L(X)=X^t\).
- 3.136*. Similar to Problem 3.136 on Page 235: Let \(\mathcal{B}=\{X_1,X_2,\ldots,X_k\}\) be a subset of a vector space \(\mathcal{V}\) and let \(L\ :\ \mathcal{V}\to \mathcal{W}\) be an isomorphism of vector spaces. Prove that if \(\mathcal{B}\) is linearly independent in \(\mathcal{V}\) then \(\{L(X_1),L(X_2),\ldots,L(X_k)\}\) is linearly independent in \(\mathcal{W}\).