**MA 2071 A '02 Practice Exam 2 Name: .**

**Section Number:.**

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

compute , where

- Find a basis for the subspace of given by all
vectors of the form with and . What is
the dimension of the subspace?
- 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 .
- Suppose
are
vectors in a vector space . Explain what it means for these vectors
to be linearly independent.
- Find a basis for the null space of the matrix given below. What is
the dimension of the null space?

2002-09-23