Chapter 4.2, Problem 51E

[M] Let a₁,…,a₅     denote the columns of the matrix A, where

$\text{A}=\left[\begin{array}{ccccc}5& 1& 2& 2& 0\\ 3& 3& 2& -1& -12\\ 8& 4& 4& -5& 12\\ 2& 1& 1& 0& -2\end{array}\right]$, $\text{B}=\left[\begin{array}{ccc}{\text{a}}_1& {\text{a}}_2& {\text{a}}_3\end{array}\right]$

Explain why a₃ and a₅ are in the column space of B.

Find a set of vectors that spans Nul A.

Let T : ℝ⁵ → ℝ⁴ be defined by T(x) = Ax. Explain why T is neither one-to-one nor onto.