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 R3 ?
| A.
 | B
 | C.
 | D.
 | E
 |
14. Let 
be a basis
for R4 and let L : R4 -> R2
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 R3 generated by the vectors
| A
 | B
 | C
 |
| D
 | E
Four vectors cannot span a subspace of R3 |
17. Let T: R2 -> R2
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 R3 generated by the eigenvectors of A corresponding
to the eigenvalue 6:
| A
 | B
 | C
 |
| D
 | E
 |
21. Let T be the linear transformation from R3
to R3 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 R4
generated by the vectors
Let N be the subspace in R4 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 |