Determining whether a transformation is onto Determining whether a transformation is onto
Showing relation between basis cols and pivot cols Showing that linear independence of pivot ...
Linear Algebra: Determinants along other rows/cols Finding the determinant by going along ...
Showing that the candidate basis does span C(A) Showing that just the columns of A associated ...
A more formal understanding of functions A more formal understanding of functions
Vector Transformations Introduction to the notion of vector transformations
Linear Transformations Introduction to linear transformations
Expressing a Projection on to a line as a Matrix Vector prod Expressing a Projection on to a ...
Matrix Vector Products as Linear Transformations Matrix Vector Products as Linear Transformations
Image of a subset under a transformation Exploring what happens to a subset of the domain ...
Linear Transformations as Matrix Vector Products Showing how ANY linear transformation can be ...
im(T): Image of a Transformation Showing that the image of a subspace under a transformation ...
Preimage of a set Definition of preimage of a set
Preimage and Kernel Example Example involving the preimage of a set under a transformation. ...
Sums and Scalar Multiples of Linear Transformations Sums and Scalar Multiples of Linear ...
More on Matrix Addition and Scalar Multiplication More on Matrix Addition and Scalar ...
Linear Transformation Examples: Scaling and Reflections Creating scaling and reflection ...
Linear Transformation Examples: Rotations in R2 Linear Transformation Examples: Rotations in R2
Rotation in R3 around the X-axis Construction a rotation transformation in R3
Unit Vectors What unit vectors are and how to construct them
Introduction to Projections Determining the projection of a vector on s line
Compositions of Linear Transformations 1 Introduction to compositions of Linear Transformations
Compositions of Linear Transformations 2 Providing the motivation for definition of matrix ...
Linear Algebra: Matrix Product Examples Example of taking the product of two matrices