Homework for Subspaces

1. Null Space

• Examples:
  • From http://linear.pugetsound.edu/html/section-HSE.html, read Example CNS1 and Example CNS2.
    Note:
    • Beezer uses the notation $\mathcal{N}(A)$ for $\textrm{Nul}(A).$ We will continute to use the latter.
    • We will continue to use parametric form for our solutions when describing $\textrm{Nul}(A).$ For example, our solution to Example CNS1 would be $$\textrm{Nul}(A) = \left\{ \ x_3 \left[\begin{array}{c} -2 \\ 3 \\ 1 \\ 0 \\ 0 \\ \end{array}\right] + x_5 \, \left[\begin{array}{c} -1 \\ -4 \\ 0 \\ -2 \\ 1 \\ \end{array}\right] \ \middle\vert \ x_3 , x_5 \in \mathbb{R} \ \right\}.$$
• Homework:
  • From http://linear.pugetsound.edu/html/section-HSE.html, do Exercises HSE.C30 and HSE.C31. Put your solutions in parametric form.