Cambridge Additional Mathematics

Vectors (Chapter 11) 301 c Find when the car is i due north ii due west of the observation point (0,0). d Plot the car’s positio ...

x y 302 Vectors (Chapter 11) Review set 11A #endboxedheading 1aWrite the given vectors in component form and in unit vector form ...

Vectors (Chapter 11) 303 11 LineLhas equation r= μ 3 ¡ 3 ¶ +t μ 2 5 ¶ a Locate the point on the line corresponding to t=1. b Exp ...

304 Vectors (Chapter 11) 7 When an archer fires an arrow, he is suddenly aware of a breeze which pushes his shot off-target. The ...

Matrices 12 Contents: A Matrix structure B Matrix operations and definitions C Matrix multiplication D The inverse of a 2£2 matr ...

306 Matrices (Chapter 12) Opening problem #endboxedheading Aakriti owns a stationery shop. She sells two brands of pen, in three ...

Matrices (Chapter 12) 307 Amatrixis a rectangular array of numbers arranged inrowsandcolumns. Each number within a matrix has a ...

308 Matrices (Chapter 12) Example 1 Self Tutor Lisa goes shopping at store A to buy 2 loaves of bread at $ 2 : 65 each, 3 litres ...

Matrices (Chapter 12) 309 4 Over a long weekend holiday, a baker produced the following food items: On Friday he baked 40 dozen ...

310 Matrices (Chapter 12) MATRIX SUBTRACTION Suppose Thao’s stock levels were 0 @ 29 51 19 31 28 32 40 17 29 1 Aand her sales ma ...

Matrices (Chapter 12) 311 EXERCISE 12B.1 1 If A= μ 34 52 ¶ , B= μ 6 ¡ 3 ¡ 21 ¶ , and C= μ ¡ 37 ¡ 4 ¡ 2 ¶ , find: a A+B b A+B+C c ...

312 Matrices (Chapter 12) 8aFor A= μ ¡ 10 15 ¶ , B= μ 34 ¡ 1 ¡ 2 ¶ , and C= μ 4 ¡ 1 ¡ 13 ¶ , find (A+B)+C and A+(B+C). b Prove t ...

Matrices (Chapter 12) 313 EXERCISE 12B.2 1 If B= μ 612 24 6 ¶ , find: a 2 B b^13 B c 121 B d ¡^12 B 2 If A= μ 235 164 ¶ and B= μ ...

314 Matrices (Chapter 12) NEGATIVE MATRICES ThenegativematrixA, denoted¡A, is actually¡ 1 A. ¡Ais obtained fromAby reversing the ...

Matrices (Chapter 12) 315 2 FindXin terms ofA,B, andCif: a X+B=A b B+X=C c 4 B+X=2C d 2 X=A e 3 X=B f A¡X=B g^12 X=C h 2(X+A)=B ...

316 Matrices (Chapter 12) 2aShow that the sum ofw,x,y, andzis given by ¡ wxyz ¢ 0 B @ 1 1 1 1 1 C A. b Represent theaverageofw,x ...

Matrices (Chapter 12) 317 Pn r=1 means the sum from r=1 to r=n. Lisa’stotal costat Store A is $ 12 : 30 , and at store B is $ 11 ...

318 Matrices (Chapter 12) Example 6 Self Tutor For A= ¡ 135 ¢ , B= μ 135 213 ¶ , and C= 0 @ 10 23 14 1 A, find: a AC b BC a Ais ...

Matrices (Chapter 12) 319 7 At a fair, tickets for the Ferris wheel are $ 12 : 50 per adult and $ 9 : 50 per child. On the first ...

320 Matrices (Chapter 12) b Now let A= μ ab cd ¶ , B= μ pq rs ¶ , and C= μ wx yz ¶ . Prove that in general, A(B+C)=AB+AC. c Use ...