1. Suppose that
Which of these subsets of the vector space R^{4} are subspaces?
A. None  B. X only  C. Y and Z only 
D. X, Y, and Z  E. None of these 
2. Let
Which of the follwing matrices represents the
composition T_{1}(T_{2}) with respect to the
standard bases for R^{2} .
A.
 B.
 C.

D.
 E.

3. If b is not 0 and adbc is not 0 then
A. 2  B. 2b  C. 0  D. 2b  E. 2 
4. Suppose T: R^{3} > R^{3}
is the linear transformation defined by
Which is the following is equal to
A
 B
 C
 D
 E
does not exist 
5. Which of the vectors
are orthogonal to the vector
and have length less than 4?
A. y only  B. z only  C. x and y only  D. x and z only  E. None of these 
6. What is the value of c for which the vectors
are orthogonal?
A. 5/7  B. 4/7  C. 3/7  D.2/7  E. 1/7 
7. If
what is the determinant of S^{1}?
8. Which of the following is a necessary and sufficient
condition for the vector
to belong to the subspace of R^{3}
generated by the vectors
A. a  3 b 4 c = 0  B. 2 a 4 b  3 c = 0  C. 3a  2 b  2 c = 0 
D. 4 a  3 b 2 c = 0  E. 5 a  7 b  c = 0. 
9. Let T: R^{2} > R^{2} be defined by
Which of the following is an equation of the line
that is mapped onto itself by T?
A. yx = 0  B. 2 x + y = 0  C.x+4y = 0  D. x + 2 y = 0  E. 4 x  y = 0 
10. What is the kernel of the linear transformation
A
 B.
 C.

D.
 E.

11. What is the inverse of the matrix
A
 B.
 C.

D.
 E.
