Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Im(t): Image of a Transformation

9th - 10th
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...
Instructional Video
Khan Academy

Khan Academy: Image of a Subset Under a Transformation

9th - 10th Standards
Exploring what happens to a subset of the domain under a transformation
Instructional Video
Khan Academy

Khan Academy: Matrix Vector Products as Linear Transformations

9th - 10th Standards
Video first shows that matrix vector multiplication is another way to represent a transformation and then shows that matrix vector products are linear transformations.
Instructional Video
Khan Academy

Khan Academy: Linear Algebra:sums and Scalar Multiples of Linear Transformations

9th - 10th
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...
Instructional Video
Khan Academy

Khan Academy: Sums and Scalar Multiples of Linear Transformations

9th - 10th
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...
Instructional Video
Khan Academy

Khan Academy: Linear Transformations as Matrix Vector Products

9th - 10th Standards
A video showing how any linear transformation can be represented as a matrix vector product.
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Linear Transformations: Scaling and Reflections

9th - 10th Standards
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]