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Due Wednesday February 8, in class

• Solution Manual: Chapter 2; Chapter 3
• Section 2.3
  • Read Section 2.3. WeBWorK reading question due January 27 @ 8:50 am.
  • Watch Lecture 2: Elimination with matrices of the MIT OpenCourseWare series
  • In class: 16*. Final due date: February 6.
    • 16*. Follow the directions for Problem 16 in Problem Set 2.3, with the following parts:
      • (a) \(X\) is three times as old as \(Y\) and their ages add to \(36\).
      • (b) Use the two points \((2,4)\) and \((4,10)\).
  • Homework: 1, 3-5, 7, 8, 11, 13, 14, 16, 18, 22, 25, 26, 28, 29
  • Hand In: 4* (include solution to #3), 16**, 26*:
    • 4*. Follow the directions for Problem 4 in Problem Set 2.3, but use \({\bf b} = (1,1,0)\)
    • 16**. Follow the directions for Problem 16 in Problem Set 2.3, with the following parts:
      • (a) \(X\) is one and a half times as old as \(Y\) and their ages add to \(45\).
      • (b) Use the two points \((2,2)\) and \((4,-2)\).
    • 26*. Follow the directions for Problem 26 in Problem Set 2.3, but use \(A = \left[\matrix{2& 5\cr 1&3}\right]\).
• Section 2.4
  • Read Section 2.4. WeBWorK reading question due January 30 @ 8:50 am.
  • Watch Lecture 3: Multiplication and inverse matrices of the MIT OpenCourseWare series
  • In class: 21*, 32. Final due date: February 8.
    • 21*. Follow the directions for Problem 21 in Problem Set 2.4, with the matrix \[A = \left[\matrix{0&-1&0&0\cr 0&0&-1&0\cr 0&0&0&-1\cr 0&0&0&0}\right]\]
  • Homework: 1, 2, 4, 6, 7, 9, 10, 11, 14, 15, 17, 18, 19, 20, 22, 26, 29, 32, 35
  • Hand In: 10*, 21**, 29*:
    • 10*. Let \[A = \left[\matrix{a&b&c\cr d&e&f\cr g&h&k}\right].\] Row 1 of \(A\) is added to row 3 to produce \(EA\). Then \(F\) adds row 2 of \(EA\) to row 1 of \(EA\), the result is \(F(EA)\)
      • (a) Compute \(EA\) and then \(F(EA)\) (you first need to decide what the matrices \(E\) and \(F\) are).
      • (b) Do those steps in the opposite order, that is, first add row 2 of \(A\) to row 1 by computing \(FA\). Then add row 1 of \(FA\) to row 3 of \(FA\) by computing \(E(FA)\).
      • (c) What law is not obeyed by matrix multiplication?
    • 21**. Follow the directions for Problem 21 in Problem Set 2.4, with the matrix \[A = \left[\matrix{0&-2&0&0\cr 0&0&-2&0\cr 0&0&0&-2\cr 0&0&0&0}\right]\]
    • 29*. Follow the directions for Problem 29 in Problem Set 2.4, with the matrix \[A = \left[\matrix{2&-2&3\cr 4&2&-1\cr -6&2&5}\right]\]
• Section 2.5
  • Read Section 2.5. WeBWorK reading question due February 1 @ 8:50 am.
  • In class: 25*. Final due date: February 13.
    • 25*. Follow the directions for Problem 25 in Problem Set 2.5, with the matrices \[A = \left[\matrix{3&1&1\cr 1&3&1\cr 1&1&3}\right]\ \mbox{and}\ B = \left[\matrix{3&-1&-1\cr -1&3&-1\cr -1&-1&3}\right]\]
  • Homework: 1, 3, 5, 6, 7, 11, 12, 17, 19, 21, 23, 24, 25, 27, 30, 32, 35, 36
  • Hand In: 17*, 27*, 30*:
    • 17*.
      • (a) What \(3\) by \(3\) matrix \(E\) has the same effect as these steps? Subtract 2 times row 1 from row 2, subtract 3 times row 1 from row 3, then subtract row 2 from row 3.
      • (b) What single matrix \(L\) has the same effect as these three reverse steps? Add row 2 to row 3, add 3 times row 1 to row 3, then add 2 times row 1 to row 2.
    • 27*. Follow the directions for Problem 27 in Problem Set 2.5, with the matrices \[A = \left[\matrix{1&0&0\cr 3&1&5\cr 0&0&1}\right]\ \mbox{and}\ A = \left[\matrix{1&1&1\cr 1&3&3\cr 1&3&5}\right]\]
    • 30*. Follow the directions for Problem 30 in Problem Set 2.5, with the matrices \[A = \left[\matrix{a&-b&b\cr -a&a&-b\cr a&-a&a}\right]\ \mbox{and}\ C = \left[\matrix{3&c&c\cr c&c&c\cr 9&5&c}\right]\]
• Section 2.6
  • Read Section 2.6. WeBWorK reading question due February 3 @ 8:50 am.
  • Watch Lecture 4: Factorization into A = LU of the MIT OpenCourseWare series
  • In class: 13*. Final due date: February 17.
    • 13*. Follow the directions for Problem 13 in Problem Set 2.6, with the matrix \[A = \left[\matrix{a&c&d&b\cr a&b&b&b\cr a&b&c&c\cr a&b&c&d}\right]\]
  • Homework: 1, 3, 4, 6, 7-9, 11, 12, 14, 15, 16, 19, 23
  • Hand In: 7*, 13**, 16*:
    • 7*. Follow the directions for Problem 7 in Problem Set 2.6, with the matrix \[A = \left[\matrix{1&1&-4\cr 3&2&-10\cr -1&1&3}\right]\]
    • 13**. Follow the directions for Problem 13 in Problem Set 2.6, with the matrix \[A = \left[\matrix{a&d&b&c\cr a&b&b&b\cr a&b&c&c\cr a&b&c&d}\right]\]
    • 16*. Follow the directions for Problem 16 in Problem Set 2.6, with the matrices \[L = \left[\matrix{1&0&0\cr 3&1&0\cr -1&-2&1}\right]\ \mbox{and}\ U = \left[\matrix{1&1&-4\cr 0&-1&2\cr 0&0&3}\right]\ \mbox{and the vector}\ {\bf b} = \left[\matrix{8\cr 21\cr -8}\right]\]