Chapter 4: Q7E (page 191)
Suppose a \({\bf{4}} \times {\bf{7}}\) matrix A has four pivot columns. Is \({\bf{Col}}\,A = {\mathbb{R}^{\bf{4}}}\)? Is \({\bf{Nul}}\,A = {\mathbb{R}^{\bf{3}}}\)? Explain your answers.
Short Answer
\({\rm{Col}}\,A = {\mathbb{R}^4}\), \({\rm{Nul}}\,A \ne {\mathbb{R}^3}\)