Linear Algebra is the of study linear sets of equations, and the various ways you can transform them. Manipulation of matrices and determinants are a major part of the subject. Linear algebra has many practical applications, especially in physics and engineering.

Students who take Linear Algebra must have taken or currently take A.P. Calculus or Analysis I. It is a one-semester course.

Topics include:

• Matrices and Systems of Linear Equations
  • Gaussian Elimination
  • Linear Independence
  • Matrix Operations
• Determinants
• Geometry of Vector Spaces in Rⁿ
  • Arithmetic
  • Dot Product
  • Cross Product
  • Lines, Planes, Spaces
  • Subspaces
  • Dimension
  • Basis
• Vector Spaces
  • Properties
  • Subspaces
  • Linear Independence
  • Basis and Coordinates Change of Basis
  • Inner-Product Spaces
  • Orthogonal Bases Gram-Schmidt Process
• Linear Transformations
  • Properties
  • Kernal and Range
  • Geometry of Transformations from R² to R²
  • Transformations from Rⁿ to R^m
  • Matrices of Linear Transformations
  • Similarity Transformations and Diagonalization
• Eigenvalues
• Least-Squares
  • Orthogonal Projections Onto Space
  • Solutions to Overdetermined Systems