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Due Monday November 25, in class

• Section 7.3
  • Read Section 7.3.
  • Worked example (group work): TBA 3*. Final due date: May 3.
    • 3*. Follow the directions for Problem 3 in Problem Set 7.3, with \[A_0 = \left[\matrix{-1&0&4\cr 0&1&2}\right].\]
  • Homework: TBA 1, 3-5
  • Hand In: TBA 3**, 4*:
    • 3**. Follow the directions for Problem 3 in Problem Set 7.3, with \[A_0 = \left[\matrix{-1&3&4\cr -3&-1&1}\right].\]
    • 4*. Follow the directions for Problem 4 in Problem Set 7.3, with \[A = \left[\matrix{2&2&1&0\cr 1&-1&0&1\cr 1&0&-2&-1}\right].\]
• Section 8.1
  • Read Section 8.1.
  • Watch Lecture 30: Linear Transformations and their matrices of the MIT OpenCourseWare series.
  • Worked example (group work): TBA 8*.
    • 8*. Find the range and kernel (like the column space and nullspace) of \(T\):
      • (a) \(T(v_1,v_2) = (0,v_1+v_2)\)
      • (b) \(T(v_1,v_2,v_3) = (v_2,v_3)\)
      • (c) \(T(v_1,v_2) = (v_2,0)\)
      • (d) \(T(v_1,v_2) = (v_2,v_2)\)
  • Homework: TBA 3, 4, 6, 7, 8, 10, 12, 13, 14, 17
  • Hand In: TBA 8**, 14*:
    • 8**. Find the range and kernel (like the column space and nullspace) of \(T\):
      • (a) \(T(v_1,v_2) = (v_1-2v_2,0)\)
      • (b) \(T(v_1,v_2,v_3) = (v_3,v_1)\)
      • (c) \(T(v_1,v_2,v_3) = (0,v_1,0)\)
      • (d) \(T(v_1,v_2,v_3) = (v_1,v_1+v_2,v_2)\)
    • 14*. Follow the directions for Problem 14 in Problem Set 8.1, with \[A = \left[\matrix{4&3\cr 3&2}\right].\]
• Section 8.2
  • Read Section 8.2.
  • Worked example (group work): TBA 10*.
    • 10*. Follow the directions for Problem 10 in Problem Set 8.2, with \[T({\bf v}_1) = {\bf w}_1+{\bf w}_2,\ T({\bf v}_2) = {\bf w}_2+ {\bf w}_3,\ T({\bf v}_3) = {\bf w}_3.\]
  • Homework: TBA 1, 5, 6, 8, 10, 11, 12, 14, 15, 17, 18, 20, 30
  • Hand In: TBA 10**, 15*, 30*:
    • 10**. Follow the directions for Problem 10 in Problem Set 8.2, with \[T({\bf v}_1) = {\bf w}_1+{\bf w}_3,\ T({\bf v}_2) = {\bf w}_1 + {\bf w}_2 + {\bf w}_3,\ T({\bf v}_3) = {\bf w}_1.\]
    • 15*. Follow the directions for Problem 15 in Problem Set 8.2, with
      • (a) \(M\) transforming \((1,0)\) to \((a,b)\) and \((0,1)\) to \((c,d)\)
      • (b) \(N\) transforming \((r,s)\) to \((1,0)\) and \((t,u)\) to \((0,1)\)
      • Answer part (c) with this \(N\) (condition is on \(r, s, t, u\)).
    • 30*. Follow the directions for Problem 30 in Problem Set 8.2, but with \(S\) reflection across the \(x\)-axis.
• Section 8.3
  • Read Section 8.3.
  • Worked example (group work): TBA 2*.
    • 2*. Follow the directions for Problem 2 in Problem Set 8.3, with \(A_1 = \left[\matrix{0&3\cr 0&0}\right]\) and \(A_2 = \left[\matrix{-2&2\cr -2&2}\right]\). (For each part solve a system found by computing \(A_iB_i\) and \(B_iJ\) for \(B_i = \left[\matrix{a&b\cr c&d}\right]\), then setting the two products equal. Your matrices \(B_i\) will not be unique.)
  • Homework: TBA 2, 3, 4
  • Hand In: TBA 2**:
    • 2**. Follow the directions for Problem 2 in Problem Set 8.3, with \(A_1 = \left[\matrix{0&5\cr 0&0}\right]\) and \(A_2 = \left[\matrix{-3&9\cr -1&3}\right]\). (For each part solve a system found by computing \(A_iB_i\) and \(B_iJ\) for \(B_i = \left[\matrix{a&b\cr c&d}\right]\), then setting the two products equal. Your matrices \(B_i\) will not be unique.)