Topic 
Time 
Comments 
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The Method of
Elimination 
5 min 40 sec 
Stepbystep procedure for a 3 by 3
system. 

Matrix Addition 
2 min 17 sec 
Adds 3 by 2
matrices. 

Scalars and Scalar Multiplication 
3 min 12 sec 
Scalar quantities and multiplication of
a matrix by a scalar. 

Matrix Differences (subtraction) 
2 min 38 sec 
Subtraction of matrices. 

Linear Combinations 
5 min 6 sec 
Scalar multiples with addition or
subtraction of matrices. 

Dot Product 
1 min 40 sec 
Uses a pair of
4vectors. 

Matrix
Multiplication 
3 min 13 sec 
Uses rowbycolumn
computation. 

MatrixVector
Product 
1 min 57 sec 
Uses a linear
combination of
columns format. 

Matrix Transformations 
7 min 25 sec 
Functions defined by matrixvector
products. 

Matrix Inverse 
15 min 23 sec 
Reversing the effect of matrix
multiplication, when possible. 

Reduced Row Echelon Form (easy) 
4 min 20 sec 
Stepbystep on an
3 by 4 matrix. 

Reduced Row Echelon Form (typical) 
7 min 12 sec 
Stepbystep on an
4 by 4 matrix. 

Solving a 3 by 3 Linear System 
4 min 50 sec 
Stepbystep solution of 3 equations in
3 unknowns. 

Solving a Homogeneous System 
4 min 49 sec 
Stepbystep on a system of 3 equations
in 4 unknowns. 

Determinants of Small Matrices
(Computing Determinants of 2 by 2 and 3 by 3 Matrices) 
5 min 57 sec 
Stepbystep development with examples
and quizzes. 

Determinants by Expansion. 
12 min 17 sec 
Determinants as a linear combination of
determinants of submatrices. 

Determinants Using Row Operations 
10 min 29 sec 
Computing the determinant using row
operations. 

An Application of Determinants 
5 min 42 sec 5 min 58
sec
6 min 1 sec 
The Area of a Parallelogram by
Determinants and the Method of Elimination 
Example
1
Example 2
Example 3 
Span Part 1 
7 min 49 sec 
The span of a set. 

Span Part 2 
16 min 57 sec 
When is a quantity in the span of a
set? 

Closure 
16 min 53 sec 
When is a set closed? 

Linear Independence/Dependence 
17 min 51 sec 
Is there a set of coefficients not all
zero so that a linear combination of quantities gives zero? 

A Discussion about Eigenvalues and
Eigenvectors 
9 min 43 sec 
Geometric and algebraic introduction. 

Computing Eigenvalues and Eigenvectors
of a 2 by 2 Matrix 
6 min 2 sec 
Stepbystep computation 

Computing Eigenvalues and Eigenvectors
of a 3 by 3 Matrix 
8 min 7 sec 
Stepbystep computation with repeated
eigenvalue 

Computing Eigenvalues and Eigenvectors
of a 3 by 3 Matrix
(a second example) 
9 min 
Stepbystep computation with repeated
eigenvalue 
