MT132 (M132): Linear Algebra

Tutor Marked Assignment

The TMA covers only chapters 1 and 2. It consists of 4 questions, each question is worth 10 marks. Please solve each question in the space provided. You should give the details of your solutions and not just the final results.

Q−1: Answer each of the following as True or False justifying your answers:

a) [2 marks] If |A| = 1, then AX = O could have more than one solution.

b) [2 marks] Any square matrix A can be written as a sum of symmetric and skew-symmetric matrices.

c) [2 marks] If A is an n×n nonsingular matrix, then A5AT is also nonsingular matrix.

d) [2 marks] If A is an n×n nonsingular matrix such that A-1 = A, then A10 = In.

e) [2 marks] If X1, X2 and X3 are linearly dependent vectors in R3, then X3 is a linear combination of X1 and X2.

Q−2: Consider the linear system: .

a) [3 marks] Find |A|, A is the coefficient matrix for the linear system.

b) [2 marks] If possible, find the inverse of A.

c) [3 marks] Solve the linear system.

d) y + z = 0. Is the new linear system consistent? Explain your answer.[2 marks] Change the third equation in the linear system to x

Q¬−3: Let .

a) [6 marks] Find the matrix A.

b) [4 marks] Find |2A3ATA-1|.

Q−4: Let be a set of vectors in R3.

a) [4 marks] Determine whether the vectors in S are linearly independent.

b) [6 marks] Write, if possible, the vector as a linear combination of the vectors in S.

Arab Open University

Faculty of Business Studies

B203A- Business Functions in Context I

Second Semester 2017-18- Tutor Marked Assessment

PART A: Inventory Management/ ABC analysis (50 marks)

The Dynaco Company stocks a variety of parts and materials it uses in its manufacturing processes. Recently, as demand for its finished goods has increased, management has had difficulty managing parts inventory; they frequently run out of some crucial parts and seem to have an endless supply of others. In an effort to control inventory more effectively, they would like to classify their inventory of parts according to the ABC approach.

Following is a list of selected parts and the annual usage and unit value for each:

Item number Annual usage (items/year) Unit cost ($) Item number Annual usage

(items/year) Unit cost ($)

1 36 350 16 60 $ 610

2 150 30 17 120 20

3 50 23 18 270 15

4 300 45 19 45 50

5 18 1,900 20 19 3,200

6 500 8 21 910 3

7 710 4 22 12 4,750

8 80 26 23 30 2,710

9 344 28 24 24 1,800

10 67 440 25 870 105

11 510 2 26 244 30

12 682 35 27 750 15

13 95 50 28 45 110

14 10 3 29 46 160

15 820 1 30 165 25

B203A TMA Second 2017-18.docx.pdf Saved to Dropbox Mar 6, 2018 at 10@45 PM

Required: Classify the inventory items according to the ABC approach using dollar value of annual demand. What recommendations would you give The Dynaco Company? (150

words)

PART B: Supply network (50 marks, 500 words)

Taking a recent purchase as an example, write an essay to discuss the supply network of your product from raw material

until it arrives to the consumer. You are required to cover the following points in your essay/presentation:

1. Company overview, product overview, major competitors.

2. Stages of the product supply chain or network design, location of raw material in relation to the manufacturer, distributor, retailer and consumer, etc.

3. The relationship between suppliers and customers (first tier, second tier, etc.., horizontal or vertical integration (if any), levels of inventory and where it’s held.

4. Explanation of any problems and suggestions for further improvements of the supply chain.