Recall that the columns of a matrix are the result of multiplying the basis vectors by the matrix. For example,
![{\displaystyle \left[{\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{33}\\a_{31}&a_{32}&a_{33}\end{array}}\right]\cdot \left[{\begin{array}{c}0\\1\\0\end{array}}\right]=\left[{\begin{array}{c}a_{12}\\a_{22}\\a_{32}\end{array}}\right].}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/4d31430004ff73223b4a9b366b1ed76c77b8cf1b)
