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.


Final Exam      (Chapters 1-3)         Monday, December 11, 1995
                                       6:55-8:10 pm (SI 212)

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                                                2 0 0 0
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


 

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

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



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

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

 

            2 0 
4. Let A =  1 1 . Then det(adj(A))  =

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


            1 0 
5. Let A =  0 1 and its eigenvector x = (x  x ) has

the component x  =  1.  Then another component x  = 

[A] 1   [B]  2   [C] 3   [D]  any number     

[E]  such  eigenvector does not exist






 
            2 1 
6. Let A =  0 1 and its eigenvector x = (x  x ) has

the component x  =  1.  Then the corresponding eigenvalue is 

[A] 1   [B]  2   [C]  3   [D]  any number     

[E]  such  eigenvector does not exist


 

7. Let det(A)=2 and det(B)=1. Then det((A  B )  ) =

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





8. The first component of the projection of vector (0, 1, 1) 
on vector (1, 0, 0) is 

[A]   0   [B]    1   [C]  1/2   [D]  1/4     [E]   None 



9. Find the area of the triangle determined
by the points (0, 1, 1), (1, 0, 1), and (1, 1, 0):


[A]   2   [B]    3   [C]  3 /2   [D]  5 /2    [E]   None




10. Find the equation of the plane passing through the points
(0, 1, 1), (1, 2, 0), and (1, 1, 0):

[A] x=y=0   [B] x+y-2=0   [C] x=t, y=t, z=t    [D] x+y+z-3=0   [E]   None