Chapter 1.4, Problem 20E

Exercises 17-20 refer to the matrices A and B below. Make appropriate calculations that justify your answers and mention an appropriate theorem.

A = $\left[\begin{array}{cccc}1& 3& 0& 3\\ -1& -1& -1& 1\\ 0& -4& 2& -8\\ 2& 0& 3& -1\end{array}\right]$ B = $\left[\begin{array}{cccc}1& 3& -2& 2\\ 0& 1& 1& -5\\ 1& 2& -3& 7\\ -2& -8& 2& -1\end{array}\right]$

20. Can every vector in ℝ⁴ be written as a linear combination of the columns of the matrix B above? Do the columns of B span ℝ³?