Module 4 - Introduction

Prospective teachers should be able to demonstrate an understanding of vectors in two and three dimensions and make connections to geometry, trigonometry, matrices, and determinants. Teachers should be able to solve systems of linear equations using a variety of methods: Algebraic substitution, Linear combinations, using a matrix inverse, using elementary row operations and Cramer's Rule.

Before studying this domain, it would be beneficial to review geometry and basic trigonometry.

 

Please read carefully the following summary description of this topic. Don't worry if you don't yet understand it completely, or, if you have already studied this material, check your understanding with the practice problems at the end and move on to the next topic.

 
  • A teacher will understand and apply the geometric interpretation and basic operations of vectors in two and three dimensions, including their scalar multiples and scalar (dot) and cross products.
  • A teacher will prove the basic properties of vectors (e.g perpendicular vectors have zero dot product)
  • A teacher will understand and apply the basic properties and operations of matrices and determinants (e.g. to determine the solvability of linear systems of equations)