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Due Wednesday November 6, in class

• Section 6.1
  • Read Section 6.1.
  • Watch Lecture 21: Eigenvalues and Eigenvectors of the MIT OpenCourseWare series.
  • Geogebra activity on eigenvectors (or another Geogebra activity on eigenvectors)
  • Worked example (group work): 24*.
    • 24*. Follow the directions for Problem 24 in Problem Set 6.1, with the matrix \[A = \left[\matrix{2\cr 1\cr 2}\right]\left[\matrix{1&2&1}\right]=\left[\matrix{2&4&2\cr 1&2&1\cr 2&4&2}\right].\]
  • Homework: 1, 2, 4, 6, 7, 9, 12, 13, 15, 17, 19, 24, 27, 28, 29, 32
  • Hand In: 2*, 24**, 27*:
    • 2*. Follow the directions for Problem 2 in Problem Set 6.1, with the matrices \[A = \left[\matrix{4&1\cr 3&2}\right]\quad \mbox{and}\quad A-I = \left[\matrix{3&1\cr 3&1}\right].\] Don't forget to complete the final sentence: "\(A - I\) has the ***** eigenvectors as \(A\). Its eigenvalues are ***** by \(1\)".
    • 24**. Follow the directions for Problem 24 in Problem Set 6.1, with the matrix \[A = \left[\matrix{1\cr 3\cr 1}\right]\left[\matrix{3&1&3}\right]=\left[\matrix{3&1&3\cr 9&3&9\cr 3&1&3}\right].\]
    • 27*. Follow the directions for Problem 27 in Problem Set 6.1, with the matrices \[A = \left[\matrix{1&1&1&0\cr 1&0&1&1\cr 1&1&1&0\cr 0&1&1&1}\right]\quad \mbox{and}\quad C = \left[\matrix{0&1&0&0\cr 1&0&0&0\cr 0&0&0&1\cr 0&0&1&0}\right].\]
• Section 6.2
  • Read Section 6.2.
  • Watch Lecture 22: Diagonalization and Powers of A of the MIT OpenCourseWare series.
  • Worked example (group work): 2*.
    • 2*. Follow the directions for Problem 2 in Problem Set 6.2, with \(\lambda_1 = 3, {\bf x}_1 = \left[\matrix{0\cr 1}\right], \lambda_2 = -2\ \mbox{and}\ {\bf x}_2 = \left[\matrix{-1\cr 1}\right].\)
  • Homework: 1, 2, 4, 6, 11, 12, 15-18, 21, 25, 26, 27, 34
  • Hand In: 2**, 16*, 18*:
    • 2**. Follow the directions for Problem 2 in Problem Set 6.2, with \(\lambda_1 = -1, {\bf x}_1 = \left[\matrix{3\cr 1}\right], \lambda_2 = 2\quad \mbox{and}\quad {\bf x}_2 = \left[\matrix{5\cr 2}\right].\)
    • 16*. Follow the directions for Problem 16 in Problem Set 6.2, with \( A_1 = \left[\matrix{0.7&0.8\cr 0.3&0.2}\right]\).
    • 18*. Diagonalize \(A = \left[\matrix{3&-2\cr -2&3}\right]\) and compute \(X\Lambda^kX^{-1}\) to find a formula for \(A^k\).
• Section 6.3
  • Read Section 6.3.
  • Watch Lecture 25: Symmetric matrices and positive definiteness of the MIT OpenCourseWare series.
  • Worked example (group work): 2*.
    • 2*. Follow the directions for Problem 2 in Problem Set 6.3, with \(S = \left[\matrix{4&6\cr 6&9}\right].\) (Just one matrix)
  • Homework: 1-3, 5, 7-12, 15, 14, 19, 25-29 odd, 37, 43, 49
  • Hand In: 2**, 19*, 29*:
    • 2**. Follow the directions for Problem 2 in Problem Set 6.3, with \(S = \left[\matrix{9&15\cr 15&25}\right].\) (Just one matrix)
    • 19*: Follow the directions for Problem 19 in Problem Set 6.3, with \(A = \left[\matrix{1&10^{-12}\cr 0&1-10^{-12}}\right].\)
    • 29*: Follow the directions for Problem 29 in Problem Set 6.3, with \(A = \left[\matrix{1&1\cr 0&2\cr 1&2}\right].\)