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.
The linear combination of a set of vectors is defined. Determine if a vector in R^2 is in the span of two other vectors. The span of a set of vectors is related to the columns of a matrix. (need topic: Determine if a vector in R^2 is in the span of two other vectors.)
Suggestions for in-class activities on linear combination and span of vectors in R^n. (need a topic for the general *process* of determining if a vector is in the span of a set of devtors)
Quiz from the University of Waterloo.