Youtubedia
Mathematics for Economists
Chapter 8
Introduction to matrices
Matrices, definitions
Special matrices
Row- and column vectors
Vectors
Addition, scalar multiplication and transpose
Matrix addition and scalar multiplication
Algebraic rules for matrix addition and scalar multiplication
Matrix transpose
Matrices: Problems
Problem: Construct matrix
Problem: Add matrices
Problem: Matrix equality
Problem: Add and subtract matrices
Problem: Linear combinations of 2 column vectors
Problem: Linear combinations of 3 row vectors
Problem: Linear combinations of 2 column vectors backwards
Problem: What can you say about the components of a vector?
Problem: Linear combination of 2 vectors, find the constants
Problem: Matrix transpose
Problem: Symmetric matrices
Matrix multiplication
Dot product
Matrix multiplication, dimension
Matrix multiplication, computation
Matrix multiplication, rules
Matrix multiplication: Problems
Problem: Input and output vectors
Problem: Input and output vectors
Problem: Matrix products
Problem: Matrix algebra
Problem: Matrix algebra
Problem: The distributive law for matrices
Problem: Matrix products
Problem: Idempotent matrices
Problem: Transpose matrix expressions
Problem: Find matrix
Matrix inverse, determinants and linear systems
Matrix Inverse
Linear systems of equations
Linear systems in matrix notation
Determinants
Inverse, determinants and linear systems: Problems
Problem: Determinants
Problem: Determinants
Problem: Matrix inverse
Problem: Matrix inverse
Problem: Matrix inverse
Problem: Matrix inverse and matrix transpose
Problem: Matrix equation
Problem: Matrix algebra
Problem: Linear equations
Problem: System of four equations
Problem: System of equations in matrix form
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Matrix multiplication, dimension
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Summary
If
\(A\)
is
\(n×m\)
and
\(B\)
is
\(k×l\)
then the product
\(AB\)
is defined only if
\(m=k\)
. In this case,
\(AB\)
has dimension
\(n×l\)
.
