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Due Wednesday October 30, in class

• Section 4.4
  • Read Section 4.4.
  • Watch Lecture 17: Orthogonal matrices and Gram Schmidt of the MIT OpenCourseWare series.
  • Worked example (group work): 5*.
    • 5*. Follow the directions for Problem 5 in Problem Set 4.4, with the plane \(x+2y+2z=0\).
  • Homework: 1-3, 5, 6, 8-11, 13, 15, 18, 20-22, 30, 31
  • Hand In: 5**, 15*, 31*:
    • 5**. Follow the directions for Problem 5 in Problem Set 4.4, with the plane \(x+2y+3z=0\).
    • 15*. Follow the directions for Problem 15 in Problem Set 4.4, with the matrix \(A = \left[\matrix{-2&3\cr 1&-1\cr 2&-1}\right]\) and (in part (c)) the vector \((2,4,-2)\).
    • 31*. Follow the directions for Problem 31 in Problem Set 4.4, with the matrix \[\left[\matrix{1&1&1&1&1&1&1&1\cr 1&-1&1&-1&1&-1&1&-1\cr 1&1&-1&-1&1&1&-1&-1\cr 1&-1&-1&1&1&-1&-1&1\cr 1&1&1&1&-1&-1&-1&-1\cr 1&-1&1&-1&-1&1&-1&1\cr 1&1&-1&-1&-1&-1&1&1\cr 1&-1&-1&1&-1&1&1&-1}\right].\] Use the vector \({\bf b} = (1,1,1,-1,-1,-1,1,-1)\) for the second part.
• Section 5.1
  • Read Section 5.1.
  • Watch Lecture 18: Properties of determinants of the MIT OpenCourseWare series.
  • Worked example (group work): 13*.
    • 13*. Follow the directions for Problem 13 in Problem Set 5.1, with the matrices \[A=\left[\matrix{1\cr 2\cr -1}\right]\left[\matrix{-1&2&1}\right]\mbox{ and }B=\left[\matrix{0&-1&2\cr 1&0&3\cr -2&-3&0}\right].\] Use cofactor expansions, not the methods of Section 5.2.
  • Homework: 4, 7, 8, 9-15 odd, 17-19
  • Hand In: 13**, 21*, 22*:
    • 13**. Follow the directions for Problem 13 in Problem Set 5.1, with the matrices \[A=\left[\matrix{3\cr -2\cr 1}\right]\left[\matrix{1&-1&3}\right]\mbox{ and }B=\left[\matrix{0&-1&2\cr 1&0&-3\cr -2&3&0}\right].\] Use cofactor expansions, not the methods of Section 5.2.
    • 21*. Compute the determinant of the matrix \[A=\left[\matrix{-2&1&2&-1\cr -4&5&3&1\cr -2&1&6&1\cr 2&-1&-2&2}\right].\] by expansion along your chosen rows and/or columns. Show all your work.
    • 22*. Find the matrix of cofactors \(C\) for the matrix \[A = \left[\matrix{1&2&-3\cr 2&3&-4\cr 1&2&-2}\right]\] and use this matrix \(C\) to compute the inverse of \(A\) (you will need the determinant of \(A\)).
• Section 5.2
  • Read Section 5.2.
  • Watch Lecture 19: Determinant formulas and cofactors of the MIT OpenCourseWare series.
  • Worked example (group work): 15
  • Homework: 1, 2, 5, 10, 12-14
  • Hand In: 5*, 13*:
    • 5*. Follow the directions for Problem 5 in Problem Set 5.2, with the systems \[\mbox{(a) } \matrix{2x_1&+&5x_2&=&3\cr x_1&+&4x_2&=&1}\ \mbox{ and (b) }\ \matrix{2x_1&+&x_2 & & &=& 0\cr x_1&+&2x_2 &+ &x_3 &=& 1\cr & &x_2 &+ &2x_3 &=& 0}.\]
    • 13*. Follow the directions for Problem 13 in Problem Set 5.2, with the matrices \[A = \left[\matrix{1&2&2\cr 1&2&3\cr 1&3&4}\right],\ \mbox{and}\ A = \left[\matrix{1&2&4\cr 2&2&4\cr 4&4&4}\right].\]
• Section 5.3
  • Read Section 5.3.
  • Watch Lecture 20: Cramer's Rule, inverse matrix, and volume of the MIT OpenCourseWare series.
  • Worked example (group work): 5*.
    • 5*. Follow the directions for Problem 5 in Problem Set 5.3, with the vectors \[{\bf v} = (3,1)\mbox{ and }{\bf w} = (2,4).\]
  • Homework: 5-7, 11
  • Hand In: 7:
    • 7. As in the text. Use row reduction.