Khan Academy: Image of a Subset Under a Transformation

Video shows an example of the image of a subset of a domain under a linear transformation. Example includes defining a triangle using vectors. [18:11]

Video shows an example of the image of a subset of a domain under a linear transformation. Example includes defining a triangle using vectors. [18:11]

Video lesson explaining why the antiderivative is the area under a curve. Provides an introduction to the fundamental theorem of calculus. [9:46]

Video demonstrating that the area of a parallelogram that is the image of a rectangle under a transformation is equivalent to the absolute value of the determinant of the matrix whose column vectors generate the parallelogram. Includes...

Worked example of linear regression using transformed data. Adapted from 2007 AP Statistics free response, form b, question 6, part d.

Worked example finding area under density curves.

Video first reviews what the image under a transformation is and then introduces the concept of preimage. [5:23]

Video first shows how to find the preimage of a set under a transformation. Shows visually what the preimage looks like on a graph. Explains that the kernel is the preimage of the zero vector. [15:23]

Video lesson finishing an example of how to evaluate the double integral to find the volume under a specific surface when the bounds are variable. Initially integrates with respect to x first and then solves the problem again integrating...

Video lesson showing how to compute the double integral to find the volume under a specific surface when the bounds are variable. Includes a visual representation. Shows how to set up the integral but not how to evaluate it. [9:51]