The product of a matrix times a vector is defined, and used to show that a system of linear equations is equivalent to a system of linear equations involving matrices and vectors. The example uses a 2x3 system.
Advice to instructors for in-class activities on matrix-vector multiplication and translating between the various equivalent notation forms of linear systems, and suggestions for how this topic can be used to motivate future topics.
We know how to add vectors and how to multiply them by scalars. Together, these operations give us the possibility of making linear combinations. Similarly, we know how to add matrices and how to multiply matrices by scalars. In this section we mix all these ideas together and produce an operation known as matrix multiplication. This will lead to some results that are both surprising and central. We begin with a definition of how to multiply a vector by a matrix.
Elementary quiz (five questions) on the matrix equation, to be completed by students after having watched an introductory video on the subject.