MA 2071 A '02 Practice Exam 2 Name: .

Section Number:.

1. First, find an equation for the plane in containing the origin and perpendicular to the vector . Let be the set of all points in that lie in this plane. Show that is a subspace of .

2. Let be the set of all ordered pairs, . Define the operation by Show that this definition does not satisfy property (h) given below.
Property (h) .

3. Suppose that is a linear transformation of into . Given the following information,

compute , where

4. Find a basis for the subspace of given by all vectors of the form with and . What is the dimension of the subspace?

5. Let be the subset of consisting of linear combinations of the three polynomials . First, show that is a subspace, and then determine a basis for and the dimension of .

6. Suppose are vectors in a vector space . Explain what it means for these vectors to be linearly independent.

7. Find a basis for the null space of the matrix given below. What is the dimension of the null space?

William W. Farr
2002-09-23