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