12. What are the eigenvalues of the matrix
A. {5, 1}  B. {1, 5}  C. {4,2}  D. {1, 3}  E.{ 2+i sqrt(7) , 2  i sqrt(7) 
13. Let
For which of the vectors w does {u, v, w} form
an orthogonal basis for R^{3} ?
A.
 B
 C.
 D.
 E

14. Let be a basis for R^{4} and let L : R^{4} > R^{2} be a linear transformation such that
What is the dimension of the kernel of L?
A. 0  B. 1  D. 3  E. 4 
15. Let
16. Which of the following is a basis for the
subspace of R^{3} generated by the vectors
A
 B
 C

D
 E
Four vectors cannot span a subspace of R^{3} 
17. Let T: R^{2} > R^{2}
be the linear transformation defined by
What is the matrix associated with this transformation
with respect to standard bases?
A
 B
 C

D
 E

18. Let
What is the entry on the first column of the third
row of A^{1} ?
A. 3  B. 1  C. 1/2  D. 1  E. 2 
19. Let
What is the determinant of A?
A. 2  B. 1  C. 0  D. 1  E. 2 
20. Let
Which of the following is a basis for the subspace
of R^{3} generated by the eigenvectors of A corresponding
to the eigenvalue 6:
A
 B
 C

D
 E

21. Let T be the linear transformation from R^{3}
to R^{3} whose matrix with respect to the standard bases
is
What is the value of (p, q, r)^{Transpose}
for which
A
 B
 C
 D
 E

22. What is the value of the determinant
where
A. 2  B. 1  C. 0  D. 1  E. 2 
23. Let M be the subspace in R^{4}
generated by the vectors
Let N be the subspace in R^{4} generated
by the vectors
Let V be the inersection of the subspaces M and
N. Which of the following pairs of vectors constitutes a basis
for V?
A
 B
 C
 D
 E

24. Let A be a square matrix whose characteristic
polynomial is
What is the determinant of A?
A. 1  B. 1/2  C. 0  D. 1/2  E. 1 