Chapter 4 - Vector Spaces - 4.4 Spanning Sets - True-False Review - Page 282: i

True

Let $\begin{bmatrix} a & b & c \\ 0 & d & e\\ 0 & 0 & f \end{bmatrix}$ be the vector space of $3 × 3$ upper triangular matrices We can rewrite as $aE_{11}+bE_{12}+cE_{13}+dE_{22}+eE_{23}+fE_{33}$ Hence, matrices in the set $S=E_{11},E_{12},E_{12},E_{22},E_{23},E_{33}$ span the vector space. The statement is true.