# Math 210-01: Linear Algebra: Reading Homework 1.1--1.2

1. What is Linear Algebra? : what is the ``most fundamental'' theme of linear algebra? what is one of our early goals for the course?
1. Theoretical Linear Algebra : what is the central theoretical topic of linear algebra?
2. Definition : what definition is given for linear algebra?
2. Systems of Linear Equations : who was Gauss? what did he do?
1. Introduction : what is a linear equation in \$n\$ variables? a nonlinear equation? a solution to a linear equation? a solution set?
2. Systems : what is a system of linear equations? what does the double subscript notation \$a_{ij}\$ in the book's example indicate?
1. solutions : when is a system of linear equations consistent? inconsistent?
2. number of solutions : how many solutions may there be to a linear system of equations?
3. solving a system : how does back substitution from row-echelon form work? what are equivalent systems? how may an equivalent system be produced from a given system?
3. Gaussian Elimination and Gauss-Jordan Elimination :
1. Matrices : what is a matrix? what is the augmented matrix for a system of linear equations? the coefficient matrix?
1. row operations : define elementary row operations; what is suggested when doing them?
2. solving linear systems : how are elementary row operations used to solve a linear system?
2. Row-Echelon Form : what is row-echelon form of a matrix? reduced row-echelon form?
3. Gaussian Elimination : what is Gaussian elimination with back-substitution?
1. Gauss-Jordan Elimination : how is Gauss-Jordan elimination different from Gaussian elimination? which is better?
4. Homogeneous Systems : what is a homogeneous linear system? what solution is ``obvious''?
1. solutions of homogeneous systems : what solutions are there to a homogeneous system?

Math 210-01: Linear Algebra: Reading Homework 1.1--1.2