How to find bases in various situations

Recall that a vector given as an $n$-tuple can also be written as a row vector ( $1 \times n$ matrix) or column vector ( $n \times 1$ matrix). For example, $(3,2,5)$ can also be written as $\left[\begin{array}{rrr}3&2&5\end{array}\right]$ or $\left[\begin{array}{r}3\\ 2\\ 5\end{array}\right]$. In this course, column vectors are usually the appropriate choice, as we'll discuss.