MA 2071 A '01 Final Exam Name: .
Show your work in the space provided. Unsupported answers may not
receive full credit.
William W. Farr
- Find the eigenvalues and eigenvectors of the following
matrix. You must show your work.
Then use your results to find a matrix such that is a
- Use Gauss-Jordan elimination to solve the following linear
- Suppose that is a linear transformation of
into . Given the following information,
compute , where
- Answer the following questions.
- Suppose that is a 3 by 5 matrix, and that the rank of is
2. Explain why this means that the dimension of the row space of
- Suppose that is the set of all ordered pairs which
satisfy . Explain why cannot be a subspace of
. Use the standard definitions for and .
- Suppose that is an matrix. Explain why the
following two statements are inconsistent.
- The rows of are linearly independent.
- Zero is an eigenvalue of A.
- Explain why a set of four or more polynomials in
must be linearly dependent.
- Find a basis for the column space of the matrix