Section 16.9 Worksheet:

Assignment: Page 1067: 1, 3, 7, 9, 11, 15, 16, 19, 20 (due Monday, 4/5).

1. What is a transformation of one plane into another? Describe it in words.

2. What is a one-to-one mapping?

3. In linear algebra one is frequently taught that the determinant is the volume of the unit ball (the n-dimensional ball of unit volume) under a linear transformation. Matrix multiplication is a transformation of into , and, in particular, the unit ball gets transformed into an ellipse.

   The volume of this ellipse is the same as the determinant of the matrix. It represents the ``inflation factor'' of the matrix.

   If you've got the ``linear algebra chops'', answer this: what's the image of the unit ball in (i.e., a circle!) under transformation by the matrix

   

   and what's its area?

4. Follow example 4 closely: it demonstrates how the spherical ``inflation factor'' of dV is determined.