21-241 Exam 1

Things to know:

·       Systems of linear equations

o      Coefficient matrix

o      Augmented matrix

o      Elementary Row Operations

o      Determining # of solutions

·       Row Reduction

o      Echelon form

o      Reduced echelon form

o      Pivot position

o      Pivot column

·       Vectors in R2, R3, Rn

o      Vector equations

o      Geometric description of addition and multiplication

o      Linear combinations

o      Span{v1}, Span{v1, v2}, Span{v1, v2, …, vn}

o      Standard unit vectors

·       Homogeneous linear systems

o      When are there nontrivial solutions?

o      Parametric vector form

o      Applications to non-homogeneous equations

·       Applications of linear systems

o      Economics

o      Chemistry

o      Networks

·       Linear Independence

o      Definition

o      Determining if a set of vectors is linearly independent

·       Linear Transformations

o      Matrix transformations

o      Definition of a linear transformation

o      Is a given transformation linear?

o      Standard matrix of a linear transformation