YEAR 11 GENERAL MATHEMATICS 2014 MATRICES TEST

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Matrices Test Year 11 General Maths 2014YEAR 11 GENERAL MATHEMATICS 2014 – MATRICES TESTName:Skills/25 Analysis/15SECTION A: Multiple ChoiceTOTAL:/4045 mins(10 x 1 marks 10 marks)Questions 1-6 are to be answered using the following matrices:2𝑉 [3456]71𝐼 [00]11𝑋 [42 3]5 63 1]π‘Œ [ 6 4 4𝑍 [ 40] 81. Which matrix has an order of (2 3)?A. VB. IC. XD. YE. Z2. Which statement about matrix I is false?A. I is an identity matrixB. I Y YD. I Y WC. I is a square matrixE. The order of I is (2 2)3. -2Z is equal to: 80]A. [ 8 1616B. [160]648C. [80]16 6 2]D. [12 8E. Undefined4. Which matrix product exists?A. IVB. XZC. YVD. XYE. VX 88]B. [8 32 124]C. [36 28 1 1]D. [ 2 47 1]E. [ 2 12C. 18D. 1 18E. -65. Y Z 1 1]A. [ 10 46. The det(Y) is equal to:A. 1 6Page 1 of 6B. 6

Matrices Test Year 11 General Maths 20147. If AX B, then X can be given by:A. AB-1B. BA-168. 𝑆 [2C. 𝐡 𝐴D. A-1BE. IA-1 3] is a singular matrix because:0A. It is a square matrixB. S2,2C. Its number of rows number of columnsD. Its identity matrix cannot be foundE. det(S) 029. [10 π‘₯ 1] [ ] [ ] generates the following pairs of simultaneous equations:3 𝑦 4A. π‘₯ 𝑦 1π‘₯ 3𝑦 4B. 2π‘₯ 1π‘₯ 3𝑦 4C. π‘₯ 4𝑦 0π‘₯ 3𝑦 4D. π‘₯ 13π‘₯ 𝑦 4E. π‘₯ 𝑦 13π‘₯ 𝑦 410. The linear equations π‘₯ 5𝑦 4 and 2π‘₯ 𝑦 3 can be written in matrix form as:1A. [25] [π‘₯ ] [4]1 𝑦 31 5] [π‘₯ ] [3]B. [ 2 1 𝑦 4 5 1 π‘₯ 4] [ ] [ ]C. [1 2 𝑦 31D. [25 π‘₯ 3] [ ] [ ]1 𝑦 41 5] [π‘₯ ] [4]E. [ 2 1 𝑦 3SECTION B: Short Answer1. 𝑋 [23(20 marks)11 3][andπ‘Œ 9 1 55 313]6a) The order of matrix X is (1 mark)b) The order of matrix Y is (1 mark)c) The order of matrix XY will be (1 mark)Page 2 of 6

Matrices Test Year 11 General Maths 2014d) Calculate matrix XY and show your workings. (2 marks)2. Given that8𝐿 [9 2]42𝑀 [8a) L N c) 3L (1 mark)(1 mark) 11 3𝑏] [ 5] [ π‘Ž3. If [ 8 6 10 2𝑐a) a 8] 919]𝑁 [ 2 3b) M – N (1 mark)d) 2N – 4M (1 mark) 4]then 4b) b c) c (1 1 1 3 marks)Page 3 of 6

Matrices Test Year 11 General Maths 201424. 𝑇 [24]3a) i. Find det(T):(1 mark)ii. T-1 (1 mark)b) State the name of the matrix produced when T is multiplied by its inverse.(1 mark)5. The following system of linear equations need to be solved using matrix methods:π‘₯ 2𝑦 43π‘₯ 2𝑦 12a) Write the two equations in matrix form.(2 marks)b) The solution is given by the equation X A-1C. Label your matrices accordingly. (1 mark)c) 𝑨 𝟏 [d) Find X.Page 4 of 6](1 mark)(1 mark)

Matrices Test Year 11 General Maths 2014SECTION C: Analysis (15 marks)1. Four peaches and 12 nectarines cost 2.28. At the same shop, two peaches and 14 nectarinescost 2.10. Using matrix methods, find the cost of each piece of fruit.(5 marks)2. For three seasons each year, a travel agent accommodates a certain number of people in fourdifferent tours: Tours A, B, C and D. This is shown as matrix S below. The cost ( ) per tour,and the number of brochures printed for each person’s information pack per tour, is shownbelow as matrix T.AutumnS 857040T brochureTour A2503Tour B3155Tour C3806Tour D4208a) How many people are accommodated for in Spring for Tour D? (1 mark)b) In which season do most people travel? (1 mark)Page 5 of 6

Matrices Test Year 11 General Maths 2014c) How many brochures are given in Tour B? (1 mark)d) Find matrix ST and label its rows and columns (3 marks)e) What was the total cost for Spring? (1 mark)f) How many brochures were printed in Autumn? (1 mark)g) State the value of ST2,2 and explain what it represents. (2 marks)Page 6 of 6

Matrices Test Year 11 General Maths 2014 Page 2 of 6 7. If AX B, then X can be given by: A. AB-1 B. BA-1 C. D. A-1B E. IA-1 8. [ 6 3 2 0] is a singular matrix because: A. It is a square matrix B. S 2,2 C. Its number of rows number of columns D. Its identity matrix cannot be found

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