In which of the following scenarios would you use matrix multiplication?

Matrix multiplication is particularly relevant when solving a system of equations, especially when those equations can be expressed in a linear form. In this context, matrices allow for a compact representation of a system of linear equations. For instance, a system with several equations and variables can be represented using an augmented matrix, where the coefficients of the variables are organized in rows and columns.

When using matrices, you can perform operations that lead to finding the solutions for the variables involved. For example, if you have a system represented as Ax = b, where A is the coefficient matrix, x is the vector of variables, and b is the result vector, you can manipulate these matrices using various matrix operations, including multiplication, to solve for x.

In contrast, adding two matrices or calculating the mean of data involves different operations not requiring the properties of matrix multiplication. Transformations of geometric shapes can involve matrix operations, but usually refer to different types of matrices, like transformation matrices, rather than direct multiplication in solving equations. Thus, matrix multiplication is essential in the context of solving systems of linear equations, making that choice the correct one.