Summary
• Solving linear systems of equations using Gauss Jordan
Method.
•Matrix form of equation .
•Rank of a matrix can tell us whether the system is
Inconsistent
Consistent with unique solution
Consistent with infinite solutions
Summary Matrices and Vectors
Summary Reflection and Scaling
Examples
Linear Transformation Matrices
Let A be a m · n matrix, 
and 
denote vectors in
and c be a real
number
Then
Linear Transformation Functions
Linear Transformation Example
Linear Transformation Matrix of a Linear Transformation
Given a linear transformation
the matrix of the
linear
transformation is given by
Linear Transformation Matrices and Linear
Transformations
•n ·1 Column matrix are Vectors in .
•m ·n Matrices define linear transformations to
• Adding matrices is adding linear transformations.
• Multiplying matrices is composing linear transformations.
for all
for all
