Question 1 -~ 15 marks You should be able lo answer this question after studying Unif 9. Give sufficient details of your working to make it clear that you have not wsed any software or calculafor that can perform matric manipulation. For example, in part (a), show explicitly how you calculated at least one element of each malric answer. (a) Let 11 L. . 2 011 Azl,lenl,mmz -1 3 3 10 2 -2 2 Evaluate each of the following expressions, if possible. Where evaluation is not possible, explain why not. i) AB ii) BA iii) C2 iv] BAC (v 3AB 2C. [10] ( ( ( ( (b) Use a matrix method to solve the following system of linear equations: br 4+ 8y =5 22 4y =3. [5] \fQuestion 3 - 5 marks You should be able to answer this guestion after studying Unif 9. You must use Marvimae to answer this question. I'nclude a printout or sereenshol of your Marima worksheet with your solution. Your solution should inelude a clear statement of the problem and the method used. Remember thal for good mathematical communication you should present your answer clearly. Below is a list of ingredients for my favourite cakes: Flour (in eups) | Milk (in cups) | Sugar (in cups) Angel cake 3 2 1 Victoria cake i 3 2 Rainbow cake 2 2 1 In my cupboard, T have 11 cups of flour, 15 cups of milk and 9 cups of sugar. How many Angel, Victoria and Rainbow cakes can 1 bake with these ingredients. assuming that I use all of the ingredients? (Give your answer to the nearest integer.) [5] You should model the problem as a system of three linear simultaneous equations, and then use matrices in Maxima to find the number of Angel, Victoria and Rainbow cakes. Given , Premium Led and quality Led are cloth manufactures (P) ( Q ) and Armana, Blue berry and channel ase fashion brand ( A) B (c ) Premium supplies 10% of t-sheets to Armana, 30% to Blueberry and 60% to channel Quality supplies , 30% of t-sheets to Armana, 40% ofto Blueberry and 30% to channel " Network diagram with input nodes P & Q and output nodes A, B, C are P Q 0 - 3 B O-IP 0. 4 8 0 . 3 B A 0-6p B ("1) The matrix that represents this network are Armana Blueberry Channel ] Premwem LEd (p ) 0. 10 0. 30 0- 60 Quality Ltd (Q ) 0 - 30 0 - 30 0-30 ( il) given , Premium Led produces 12800 t-shirts each month Quality Ltd produces 8: 9600 t-shuts each month calculation of t-shirts supplied every month 1 ) For Premium Lid CP ) Armana = 0-10 x 12800 = 1280 t-shirts Bluebelly = 0- 30 * 12860 = 3840 t-shirts channel = 0-60 * 12 500 = 7 680 t-shirts2 ) For Quality Led (0) Armand = 0-30 * 9600 = 3x 960 = 2880 t-shuts Blueberry - 0. 40 x96010 = 4x960 = 3840 t-shirts channel = 0-30 x960 = 3*960 = 2880 t-shirts b) Given Armana sells 45 % at London stoes = 0-45 115%% at Manchester = 0-15 40% at Newcastle = 0-40 Blueberry sells 30% at London Stores = 0- 30 70% at Manchester = 0 750 channel sells 35% at London stow = 0-35 25% at Manchester = 0:25 40% at New castle =0:40 17 Matrix Representation is London Manchester Newcastle Armand . 0. 45 0-15 0-40 Blueberry 0-30 0- 70 2 0 0-00 Newcastle 0 - 35 40-250 0- 40 Channel 2 Find single malux that represents the proportion of t-shirts each manufactured P & & supplies to each city London, Manchester, Newcastle A B M N 0 . 10 0- 30 0 - 60 A 0-4.5 0.15 0.40 0-30 0-70 0 a 0 - 30 0.40 0 .30 B 2X3 C 0- 35 0.25 0- 40 X 3 x3 so multiply mateix x Q y as the columns in the X matrix and lows in the Y matrix are matched we can multiplyP N a = (0.1x0 - 45 ) + (0- 3 x 0 - 3 ) + (0-6 * 0- 35 ) = 00#4 0345 b = (0. 1 x 0-15 ) + (0-3 *0 . 70) + (0-6*0- 25 ) = 0-375 C = ( 0 - 1 x 0 - 4 ) + ( 0 - 3 x 0 ) + ( 0 - 6 * 0 - 4 ) = 0-28 d = (0-3 x0.45 ) + (0.4 x0 - 3 ) 7 (0-3 x0 35 ) = 0-36 e 8 = ( 0 - 3 * 0 -15 ) + ( 0 - 4 x 0 70 ) + (0-3 * 0- 25 ) = 0 - 4 * = ( 0-3 x 0-4 ) + ( 0 - 4 x 0 ) + (0-3x 0 04 ) = 0- 24 - London Manchester Newcastle Premium 10- 345 0 : 375 0 . 28 Quality 0 - 36 0 - 24 (1) Gives Quality LAd had to recal all of its T-shirts due to some defects in manufacturing So it has maximum sales in Manchester le. 0-40 so Manchester is the most affected city by Quality Ltd's t-shirt recall due to defects