Consider the linear transformation which maps to and to .
Find the matrix which represents this transformation.
Where does this transformation map and ?
The determinant of a matrix is . What is the area of the image of a unit square under the transformation it represents?
Suppose the linear transformation sends to and to . What is the absolute value of the determinant of the matrix representing ?
A linear transformation maps the points , , , and onto , , , and , as shown.
By finding the areas of the object and image, and considering orientation, find the determinant of the matrix representing this transformation.
Consider the linear transformations for which , the image of , and , the image of , are unit vectors. Let be a linear transformation of this kind which has the additional property that the area of the parallelogram with vertices , , , and is as big as possible. What are the possible values of the measure of the angle between and for the transformation ?