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Due Wednesday December 4, in class

• Section 10.1
  • Read Section 10.1.
  • Worked example (group work): TBA.
    • 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
  • Hand In: TBA :
    • 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 10.2
  • Read Section 10.2.
  • Worked example (group work): TBA.
    • 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
  • Hand In: TBA:
    • 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.