Fall 2024

Math 3110 Linear Algebra for Engineers

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Homework 3

Due Wednesday September 11, in class
  • Section 2.2
    • Read Section 2.2.
    • Worked example (group work): 32*.
      • 32*. Follow the directions for Problem 32 in Problem Set 2.2, with the matrix \[U=\left[\matrix{1&0&a&b\cr 0&1&0&c\cr 0&0&1&0\cr 0&0&0&1}\right]\]
    • Homework: 1, 3, 7, 12, 13, 15, 17, 19, 21, 25, 29, 32-34, 39
    • Hand In: 21, 32**, 34*:
      • 21. Do the problem exactly as in the textbook.
      • 32**. Follow the directions for Problem 32 in Problem Set 2.2, with the matrix \[U=\left[\matrix{1&a&0&0\cr 0&1&b&0\cr 0&0&1&c\cr 0&0&0&1}\right]\](Don't assume you know the answer without performing the row operations)
      • 34*. Follow the directions for Problem 34 in Problem Set 2.2, with the matrices \[A=\left[\matrix{a&a&a\cr a&a&b\cr a&b&b}\right], C=\left[\matrix{c&3&c\cr 5&6&c\cr c&c&c}\right] \]
  • Section 2.3
    • Read Section 2.3.
    • Watch Lecture 2: Elimination with matrices of the MIT OpenCourseWare series
    • Worked example (group work): 10*.
      • 10*. Follow the directions for Problem 10 in Problem Set 2.3, with the following: \[L=\left[\matrix{1&0&0\cr -1&1&0\cr 1&-1&1}\right], U=\left[\matrix{1&2&3\cr 0&1&2\cr 0&0&1}\right], {\bf b}=\left[\matrix{3\cr 2\cr 1}\right].\]
    • Homework: 1-7 odd, 9-13
    • Hand In: 10**, 13*:
      • 10**. Follow the directions for Problem 10 in Problem Set 2.3, with the following: \[L=\left[\matrix{1&0&0\cr 1&1&0\cr 1&1&1}\right], U=\left[\matrix{1&2&3\cr 0&1&2\cr 0&0&1}\right], {\bf b}=\left[\matrix{1\cr 2\cr 3}\right].\]
      • 13*. Follow the directions for Problem 13 in Problem Set 2.3, but use \[A = \left[\matrix{1&2& 0\cr 2&5&1\cr 0&1&4}\right], A = \left[\matrix{a&2a& 0\cr 2a&4a+b&b\cr 0&b&b+c}\right].\]
  • Section 2.4
    • Read Section 2.4.
    • Watch Lecture 3: Multiplication and inverse matrices of the MIT OpenCourseWare series
    • Worked example (group work): 18*.
      • 18*. Follow the directions for Problem 18 in Problem Set 2.4, with the matrices \[S = \left[\matrix{1&2\cr 2&6}\right], S = \left[\matrix{2&-2&0\cr -2&6&-2\cr 0&-2&6}\right]\]
    • Homework: 1-7 odd, 11. 13, 17-19, 25-27
    • Hand In: 18**, 19*:
      • 18**. Follow the directions for Problem 18 in Problem Set 2.4, with the matrices \[S = \left[\matrix{1&-2\cr -2&8}\right], S = \left[\matrix{3&-1&0\cr -1&2&2\cr 0&2&4}\right]\]
      • 19*. Follow the directions for Problem 19 in Problem Set 2.4, with the matrices \[A = \left[\matrix{0&1&2\cr 2&0&3\cr 4&-1&2}\right], A = \left[\matrix{1&2&-1\cr 3&6&4\cr 2&2&2}\right].\]