COURSE
MATH 3191: Applied Linear Algebra. 
Fall 1995. University of Colorado Denver

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

TEXTBOOK
Elementary Linear Algebra. 7th ed. Howard Anton and Chris Rorres. Wiley, 1994.


EXAM #1     (Chapter 1)         Wednesday, September 27







                                                2 0 0 2
1. The reduced row-echelon form of the matrix   1 1 0 1    is

     1 0 0 1            0 1 0 0            1 1 1 1        1 0 0 1
[A]  0 1 0 0       [B]  1 0 0 1       [C]  0 1 0 0   [D]  0 1 0 1  [E] None



         0 1 2 3 4
2. Let   1 2 3 4 0     be an augmented matrix of a system of


linear equations. Then  x  + 3 x    equals to 


[A]   x    [B]    0    [C]   2 x  - 4   [D]  4 - 2 x       [E]  None


            2 0 
3. Let A =  1 1 . Then  tr(A+A  ) =  

[A]   1   [B]    2   [C]   3   [D]  4     [E]   None
       
        
            2 0 
4. Let A =  1 1 .  Reduce A to reduced row-echelone form B. Then tr B =

[A]   1   [B]    2   [C]   3   [D]  4     [E]   None


5. The matrix equality  A  = I  is correct

[A] for any diagonal matrix A  
[B] for any lower triangular matrix A 
[C] if A=I, or A=-I  
[D] if A is an elementary matrix
[E] The correct answer is not given by [A],[B],[C], or [D]








 
           1 0 1
6. Let A   0 1 0   and B=A  =(b   ). Then b    =
           1 0 2

[A]   1   [B]    2   [C]   3   [D]  4     [E]   None

            2 0 
7. Let A =  1 1 .  Then tr A  =

[A]   1   [B]    2   [C]   3   [D]  4     [E]   None
 

8. Let A and B be square matrices of the same sizes, A is invertible,
and B is not invertible. Which of the following matrices may be invertible:

[A] AB  [B] BA  [C] A+B  [D] ABA
[E] The correct answer is not given by [A],[B],[C], or [D]


9. Which of the following statements must be true, if all the indicated
operations can be performed:

[A]   ((A+I)  +B)   =  A  +I+B
[B]   A(BAC)=(ACA)B 
[C]   (A-B)(A+B)=AA-BB
[D]   (A+BC)(A+CB)=AA+ACB+BCA+CBBC
[E]   None



              1 2 3             1 0 0 
10. Let  A =  0 4 5   and  B =  2 3 0
              0 0 6             4 5 6 
              
Which of the following matrices is upper triangular:

[A]  (B+A )    
[B]  AB
[C]  BA
[D]  AA+BB            
[E]  B  + A