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Homework 10
- Section 7.1
- Read Section 7.1.
- Watch Lecture 29: Singular Value Decomposition of the MIT OpenCourseWare series.
- Worked example (groip work): TBA 1*.
- 1*. What are the ranks \(r\) of the following matrices? Write \(A\) and \(B\) as the sum of \(r\) pieces \({\bf uv}^t\) of rank one. We do not require orthogonality of the different \({\bf u}_i\) and \({\bf v}_j\). \[A = \left[\matrix{-1&0&1\cr -2&0&2\cr 3&0&-3}\right], \ \mbox{and}\ B = \left[\matrix{1&0&1&-1\cr 0&1&2&-2\cr 1&1&3&-3\cr 2&2&6&-6}\right].\]
- Homework: TBA 1-4, 6, 8
- Hand In: TBA 1**, 3*:
- 1**. What are the ranks \(r\) of the following matrices? Write \(A\) and \(B\) as the sum of \(r\) pieces \({\bf uv}^t\) of rank one. We do not require orthogonality of the different \({\bf u}_i\) and \({\bf v}_j\). \[A = \left[\matrix{1&2&-2&-1\cr 3&6&-6&-3\cr 2&4&-4&-2\cr 4&8&-8&-4}\right], \ \mbox{and}\ B = \left[\matrix{1&2&3&4\cr 2&4&9&16\cr 3&6&12&20\cr 1&2&6&12}\right].\]
- 3*. Follow the directions for Problem 3 in Problem Set 7.1, with \[A_1 = \left[\matrix{2&2&1&1\cr 2&2&1&1\cr 1&1&1&1}\right], \ \mbox{and}\ A_2 = \left[\matrix{1&2&2&2\cr 1&1&1&1\cr 1&3&3&3}\right].\]
- Section 7.2
- Read Section 7.2.
- Worked example (group work): TBA 4*.
- 4*. Follow the directions for Problem 4 in Problem Set 7.2, with \[A = \left[\matrix{2&0&1\cr 2&1&0}\right].\]
- Homework: TBA 1-4, 8, 11, 13, 14, 17
- Hand In: TBA 4**, 8*:
- 4**. Follow the directions for Problem 4 in Problem Set 7.2, with \[A = \left[\matrix{1&0&2\cr 1&2&0}\right].\]
- 8*. Follow the directions for Problem 8 in Problem Set 7.2, with \(A = \left[\matrix{1&4\cr 2&8}\right]\) (compute the correct matrices \(A^tA\) and \(AA^t\)).