Fall 2021

Math 3120 Introduction to Linear Algebra

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Homework 7

Due Wednesday December 8, in class
  • Section 6.3 Fourier Series: Scalar Product Spaces
    • Read Section 6.3. Do Problem 6.37. WeBWorK reading question due November 17 @ 9:45 am.
    • In class (group work): 6.38
    • Homework: 6.39, 6.40, 6.41 (use cosines), 6.43, 6.45, 6.46, 6.50, 6.51, 6.53
    • Hand In: 6.41, 6.43, 6.50
  • Section 6.4 Orthogonal Matrices
    • Read Section 6.4. Do the True/False questions (pp. 363-364). Do Problems 6.58, 6.60(b). WeBWorK reading question due November 22 @ 9:45 am.
    • In class (group work): 6.60(a), 6.73(b)
    • Homework: 6.60(c), 6.61, 6.62, 6.64, 6.67, 6.73(a)(c), 6.75, 6.76
    • Hand In: 6.61(b), 6.73(c)
  • Section 6.5 Least Squares
    • Read Section 6.5. Do Problem 6.79. WeBWorK reading question due November 29 @ 9:45 am.
    • In class (group work): 6.82, 6.85
    • Homework: 6.83, 6.86, 6.89, 6.91, 6.92, 6.93
    • Hand In: 6.86, 6.93, plus the following problem:
      • Find the least squares best fit line \(y = a + bt\) to the four points \((t,y) = (0,1),(1,6),(3,13),(4,18)\). Also compute the predicted values vector \(B_0\) of \(y\) for each of the given \(t\) values, and then compute the error vector \(B_1 = B - B_0\).
    • WeBWorK assignment due December 6 @ 11 pm
  • Section 6.6 Quadratic Forms: Orthogonal Diagonalization
    • Read Section 6.6. Do the True/False questions (pp. 391-392). Do Problems 6.95, 6.96. WeBWorK reading question due December 3 @ 9:45 am.
    • In class (group work): 6.97(a), 6.98(b), 6.102
    • Homework: 6.97(c)(e), 6.98(c)(d), 6.100, 6.104, 6.105, 6.112
    • Hand In: 6.97(e) (identify the surface type), 6.100
  • Section 6.7 The Singular Value Decomposition (SVD)
    • Read Section 6.7. Do the True/False questions (pp. 403-404). Do Problems 6.116(a), 6.117(a). WeBWorK reading question due December 6 @ 9:45 am.
    • In class (group work): 6.116(c), 6.117(e)
    • Homework: 6.116(b)(d), 6.117(c)(b)(d), 6.119(a)(b), 6.120, 6.123, 6.124
    • Hand In: none