Individual Response for Unit Analysis

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Individual Response for Unit Analysis Powered By Docstoc
					R. Ng
                                                                          Sep 29, 2008

Matrices Test review

[ Q1 taken from Finite, MHR, p 348 , Q 6 ]

    1.       Given the following matrice

                                    Rows  destination
                                    Columns  start po int
                                    1000    850 100 500 
                                     750    600 270 150 
                                                        
                                     370    220 80 430 
                                                        
                                     640    480 300 200 

      (A)          How many vehicles travel from Zone 3 (start) to Zone 1 (destination)

      (B)          How many travel from Zone 4 to Zone 1 ?

      (C)          Of the vehicles starting from Zone 2, how many remain in Zone 2 ?

      (D)          In total, how many vehicles travel to Zone 3 from a different starting point ?

      (E)          How many vehicles left Zone 1 ?

      (F)          Write the transpose of the above matrix.


    2.       (A)      Draw a network diagram corresponding to the matrix:

                   1 2 0 
                   1 0 1 
                         
                   3 1 0 
                         

             (B)      Solve for the determinant of this matrix




                      Hint:




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                                7 1
   3.         For the matrix,        
                                3 2
              (B)    Solve for the determinant of this matrix

              (C)        Solve for the inverse of this matrix

                             1
                    a b                1       d b      1  d b 
   Hint:            c d                        c a   det   c a 
                                    ad  bc                        

   4.         Solve the following matrice multiplication.

              2  4
                         9  8 3
        A   7 0 , B             
             2 10        4  6 1 
                    

        (A)         AB                                          (B)   BA

        Explain why AB is not equal to BA.



                                            103 56                          4 7
   5.         Decode the following message.        with the decoder        1 2 
                                             56 31                              

   Hint: Always place the decoder in front of the code.


   6.         Reduce each of the following matrices to reduced row echelon form.

               1 1 0             1
                                    
               2 3 4             1
               1 6  4           7
                                    
                                    


   7.         Represent the following information in a matrix and solve.

               Fund                       A              B            C
               Growth rate                10 %           12 %         18 %
               Dividend                   12 %           11 %         8%



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             (A) if Bob wants to have an average growth rate of 14 % and an
                 average dividend yield of 10 %, how should he divide the money
                 among his 3 funds ?

             Hint: is this a dependent or independent system of equations ?

               Ans : 66,666  k  50,000


             (B) If bob invest $40,000 in Fund C. How should the reminder of his
                 100,000 be invested into A and B so that he meets the desired 14
                 % growth rate and 10% dividend yield ?

               Ans : A = $ 20,000 , B = $ 40,000


             (C) What is the maximum Bob can invest in Fund C to meet his
                 desired yield / growth ?




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