Scaling matrices are mathematical tools used in linear algebra to resize objects in a coordinate system. They work by multiplying a vector by a scaling matrix, which alters the size of the object without changing its shape. For example, a scaling matrix can stretch or compress an object along the x-axis or y-axis by specific factors. In a two-dimensional space, a scaling matrix is typically represented as a 2x2 matrix, where the diagonal elements indicate the scaling factors. For instance, a scaling matrix of {2, 0, 0, 3} would double the size of an object along the x-axis and triple it along the y-axis.