Background+and+Materials

Assumed Background:
This should be used as a summative assessment and activity after a 1 to 2 week unit on linear algebra, or matrices. Students should know how to perform elementary operations on matrices, including: matrix addition, pre-multiplication, post-multiplication, multiplication by a scalar, and should be familiar with the identity matrix. Students should already know how to represent a system of equations in a matrix form, should have already performed Cramer’s rule on 2x2 and 3x3 matrices, and have experience performing Row Operations on an augmented matrix – as solution methods to systems of 2 and 3 equations. This exercise, done manually (not with a computer or calculator) will increase the connection between these seemingly disassociated techniques of solving such systems.

Guiding Questions:
What does it mean to find ‘solutions’ to a system of equations? What are the relationships between the number of variables, the number of equations, and the number of ‘Dimensions’ in a problem?

Needed Material:
A handout to each student containing the diagram below, the system of equations, and the matrix form of this system. The handout should also contain the instructions and the guiding questions.