COURSE
MATH 3191-004: Applied Linear Algebra. 
Fall 1994. University of Colorado at 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.
Note: 7th edition (not 6th) is necessary.


EXAM #1     (Chapter 1)    20% of the FINAL GRADE     Monday, September 12

Note: All exams are in class. The only materials students are allowed to 
bring to the exam are writing instruments and erasers.  




                                                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



         0 1 2 3 4
2. Let   5 6 7 8 9     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



3. Let A be a square matrix. Then  tr(A+A  ) = 2 tr(A) 

[A] for 1x1 matrix A only 
[B] for a symmetric matrix A only
[C] always  
[D] The correct answer is not given by [A],[B], or [C]


4. The matrix equality   BB-B=(B-I)B  is correct

[A] for 1x1 matrix B only 
[B] if B is a symmetric matrix 
[C] if B is a column matrix (or a column vector) 
[D] The correct answer is not given by [A],[B], or [C]


5. The matrix equality  A  = A  is correct

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










6. Which of the following statements must be true:

[A] Every system of linear equation has a solution.
[B] Matrix [ A  b ] is an augmented matrix of the linear system Ax=b.
[C] ABC=BCA=CAB for square matrices A,B, and C of the same sizes. 
[D] If matrices A and B are invertible, then A+B is invertible.


7. Let A and B be elementary matrices of the same sizes. 
Which of the following statements must be true:

[A] Matrix AB is invertible.
[B] Matrix AB is elementary.
[C] AB=BA.
[D] [A B] is a square matrix.
 

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] The correct answer is not given by [A],[B], or [C]


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+BCCB



              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 lower triangular:

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