COURSE
MATH 3191-004: Applied Linear Algebra. 
Fall 1994. University of Colorado Denver

INSTRUCTOR 
Dr. Andrew Knyazev
Office: CU (Dravo) 620G. Phone: 556-8102.
Office hours: Tue 3pm - 6pm


EXAM #3     (Chapter 5)   15% of the FINAL GRADE    Monday, November 14





                                  2 0 0 2
Let A be the following matrix     1 1 0 1   for problems 1-7.
                                  1 2 2 1
                                  2 0 0 1



1. rank(A) =   

[A]  1    [B]   2    [C]    3    [D]    4



2. Which of the following is a vector in the nullspace of A?

[A] (0 0 0 0)  [B] (0 1 0 0)  [C] (0 -1 2 0)   
[D] The correct answer is not given by [A],[B], or [C]



3. The linear system Ax=b is not consistent for b=   

[A] (0 0 0 0)  [B] (0 1 0 0)  [C] (0 -1 2 0)   
[D] The correct answer is not given by [A],[B], or [C]




4.  rank(A) - nullity(A) =   
 

[A]  1    [B]   2    [C]    3    [D]    4



5. The dimension of the subspace spanned by a first 3 rows
of A equals


[A]  1    [B]   2    [C]    3    [D]    4



6. Which of the following statements must be true:


[A] The last row of A can be expressed as a linear combination of the first 3.
[B] The last column of A can be expressed as a linear combination of the first 3.
[C] Both [A] and [B] are correct statements
[D] None of the above is correct


7. Let 4x8 matrix B = [A A]. Then nullity(B) =  


[A]  1    [B]   2    [C]    3    [D]    4


8. Let u, v and w be vectors in 10 dimensional vector space. Then  
dim(span{u,v,w}) can not be equal to

[A]  1    [B]   2    [C]    3    [D]    4


9.  Let A, B, C, and D be the following 2x2 matrices.

   2 0      1 1      1 2    2 0 
   0 2      0 1      2 1    0 1
                           
We consider A, B, C, and D as elements of the vector space of all 2x2 matrices
with real entries. Then
                            
[A] D can be expressed as a linear combination of A, B, and C.
[B] A, B, C, and D form a basis
[C] Both [A] and [B] are correct statements
[D] None of the above is correct



10. Let 

p(x) = 2x + 2, q(x) = x + x + 1, r(x) = x + 2x + 2x + 1, and t(x) = 2x + 1.

We consider p(x), q(x), r(x), and t(x) as elements of the vector space 
of all real-valued functions defined on the entire real line. Then

[A] t(x) can be expressed as a linear combination of p(x), q(x), and r(x).
[B] p(x), q(x), r(x), and t(x) form a basis
[C] Both [A] and [B] are correct statements
[D] None of the above is correct