# Individual Response for Unit Analysis by pengxiang

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```									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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