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Khan Academy
Khan Academy: Linear Algebra: Im(t): Image of a Transformation
Video first reviews the closure properties of subspaces. Shows that the image of a subspace under a linear transformation is a subspace. Connects the meaning of range to the image of the transformation. Shows that the image of the linear...
Khan Academy
Khan Academy: Image of a Subset Under a Transformation
Exploring what happens to a subset of the domain under a transformation
Khan Academy
Khan Academy: Matrix Vector Products as Linear Transformations
Video first shows that matrix vector multiplication is another way to represent a transformation and then shows that matrix vector products are linear transformations.
Khan Academy
Khan Academy: Linear Algebra:sums and Scalar Multiples of Linear Transformations
Video first defines the sum of transformations. Shows that the sum of two transformations is equal to the sum of their transformation matrices. Defines scalar multiples of linear transformations and shows that they are equal to the...
Khan Academy
Khan Academy: Sums and Scalar Multiples of Linear Transformations
This video shows that the sum of two transformations is equal to the sum of their transformation matrices. Defines scalar multiples of linear transformations and shows that they are equal to the scalar multiples of their transformation...
Khan Academy
Khan Academy: Linear Transformations as Matrix Vector Products
A video showing how any linear transformation can be represented as a matrix vector product.
Khan Academy
Khan Academy: Linear Algebra: Linear Transformations: Scaling and Reflections
Video first reviews how to find the transformation matrix using the identity matrix. Shows how to write a transformation matrix that reflects over the y-axis and scales the y-coordinates by a factor of 2. [15:13]