Understanding linear equations, their geometric interpretations, and how systems of equations relate to intersections of geometric objects.
Learn how to systematically solve systems of linear equations using augmented matrices, row operations, and echelon forms.
Understand when a system has a solution and when that solution is unique using row reduction and free variables.
Introduction to vectors, their geometric interpretation, and fundamental vector operations
Define matrices and understand matrix-vector multiplication and its linear properties
Express systems of linear equations as vector and matrix equations, and prove why systems have 0, 1, or infinitely many solutions
Understand parametric representations of lines and planes using vectors
Understand homogeneous systems Ax = 0 and their solution sets
Understand the span of vectors and when vectors are linearly independent
Understand linear transformations and their matrix representations
Understand injectivity and surjectivity of linear transformations via matrix properties