# span, basis and dimension

• Mar 20th 2011, 07:44 AM
wik_chick88
span, basis and dimension
im having a little/big problem with the whole concept of span, basis and dimension
eg. $S = \{\left(\begin{array}{cc}a&b\\c&a\end{array}\right ) \in V: a,b,c \in \Re \}$
how would i go about finding the span, the basis and the dimension of $S$?
• Mar 20th 2011, 08:54 AM
Plato
Quote:

Originally Posted by wik_chick88
im having a little/big problem with the whole concept of span, basis and dimension
eg. $S = \{\left(\begin{array}{cc}a&b\\c&a\end{array}\right ) \in V: a,b,c \in \Re \}$
how would i go about finding the span, the basis and the dimension of $S$?

Is this a basis: $\[
\left\{ {\left( {\begin{array}{*{20}c}
1 & 0 \\
0 & 1 \\

\end{array} } \right),\,\left( {\begin{array}{*{20}c}
0 & 1 \\
0 & 0 \\

\end{array} } \right),\,\left( {\begin{array}{*{20}c}
0 & 0 \\
1 & 0 \\

\end{array} } \right)} \right\}~?$
• Mar 20th 2011, 10:25 AM
HallsofIvy
$\begin{pmatrix}a & b \\ c & a\end{bmatrix}= \begin{pmatrix}a & 0 \\ 0 & a\end{pmatrix}+ \begin{pmatrix}0 & b \\ 0 & 0\end{pmatrix}+ \begin{pmatrix}0 & 0 \\ c & 0\end{pmatrix}$

It makes no sense to talk about finding the "span" of a vector space.