Matrices#
Matrices are a power tool in linear algebra. We can use them to solve linear equations, find the different properties of a vector space, and more. Because of how important matrices are in the world of linear algebra, it’s important to talk about what a matrix is and how they work. It’s also worth noting, as this can be a pain point for many math teachers, the singular form is ‘matrix’ (pronounced may-trix) and the plural form is ‘matrices’ (pronounced may-tri-ceez).
This is an example of a matrix:
\( \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)We can describe a matrix by its number of rows and columns. Therefore, we would call this a three by three matrix, $$ {3},{x},{3} $$, because it has three rows and three columns.
We often use matrices to display collections of vectors. Vectors are represented by a single column in a matrix, where each entry of that column corresponds to a component of the vector. For example:
\( \begin{pmatrix} 2 & 1 & 5 & -3\\ 1 & 2 & -5 & 8\\ -4 & 1 & 5 & 6 \end{pmatrix} \)The matrix above has four vectors \( \{<}\{2},\{1},\{-4}\{>} \)