Section 9 Week 1 Learning Goals

Here are the knowledge and skills you should master by the end of this first, shorter week.

9.1 Solving Linear Equations

I should be able to do the following tasks:

  • Identify linear systems from nonlinear systems
  • Create a linear system to solve a variety of applied scenarios
  • Convert between a linear system and an augmented matrix
  • Row reduce an augmented matrix into Row Echelon Form (REF) and Reduced Row Echelon Form (RREF)
  • Use REF to determine whether a linear system is consistent or inconsistent
  • Use REF to determine whether a consistent system has a unique solution or an infinite number of solutions
  • Use RREF to find explicit equations for the solution set of a consistent system

9.2 RStudio

I should be able to do the following tasks:

  • Log in to Macalester’s RStudio server
  • Upload R Markdown files to RStudio
  • Knit R Markdown to produce HTML
  • Use RStudio to create vectors and matrices
  • Use the rref command from pracma to solve a linear system

9.3 Vocabulary

I should know and be able to use and explain the following terms:

  • elementary row operation (and be able to state them)
  • augmented matrix
  • REF and RREF
  • pivot position
  • basic variable (pivot variable)
  • free variable
  • consistent system and inconsistent system

9.4 Conceptual Thinking

I should understand and be able to perform the following conceptual tasks:

  • Model 2-dimensional linear systems as the intersections of lines
  • Model 3-dimensional linear systems as the intersections of planes