1.2 Gauss-Jordan elimination
Definition 1. A matrix is in reduced row-echelon form if it satisfies all of the following conditions:
(1) If a row has nonzero entries, then the first nonzero entry is a 1, called a leading 1, or pivot.
(2) If a column contai
Math 306 Linear Algebra
fall 2016 syllabus
Class Location: Herman 103, MWF 2:002:50 PM
Instructor: T. Alden Gassert
Office: Herman 309B
Email: [email protected]
Office Hours: MWF 10:3011:30 AM, MW 3:004:00 PM, and by appointment.
Math Center: M 11:00
1.3 vector equations
We have already seen that a system of linear equations may be solved by solving a matrix equation of the
form Ax = b. But why is that the case?
Theorem 1 (Lay, Ch. 1, Th. 3). If A = [aij ] is an m n matrix with columns a1 , . . . , an
1.7 Linear independence
Definition 1. A set of vectors cfw_a1 , . . . , ak is linearly independent if the vector equation
x1 a1 + + xk ak = 0
has exactly one solution, the trivial solution, x1 = x2 = = xk = 0.
Definition 2. If there are non-trivial s
1.4 The equation Ax = b
Theorem (Lay, Ch. 1, Th. 4). Let A be an m n matrix. Then the following are equivalent (either all
true or all false)
a. For each b Rm , the equation Ax = b has a solution.
b. Each b Rm is a linear combination of the columns of A.
1.1 Introduction to linear systems
Linear algebra finds its origins in the study of linear systems of equations. Some familiar examples
of linear equations are
ax + by = c
ax + by + cz = d.
There is no limit to the number of variables a linear equatio