Cambridge Additional Mathematics

Matrices (Chapter 12) 321 Example 7 Self Tutor Expand and simplify where possible: a (A+2I)^2 b (A¡B)^2 a (A+2I)^2 =(A+2I)(A+2I) ...

322 Matrices (Chapter 12) 4aIf A= Ã 1 2 1 2 1 2 1 2 ! , determine A^2. b Comment on the following argument for a 2 £ 2 matrixAsu ...

Matrices (Chapter 12) 323 The real numbers 5 and^15 are calledmultiplicative inversesbecause when they are multiplied together, ...

324 Matrices (Chapter 12) Just as the real number 0 does not have a multiplicative inverse, some matrices do not have a multipli ...

If , the matrix is singular. det = 0A A Matrices (Chapter 12) 325 6 Suppose A= μ ab cd ¶ and B= μ wx yz ¶ . a Find: i detA ii de ...

326 Matrices (Chapter 12) FURTHER MATRIX ALGEBRA In this section we consider matrix algebra with inverse matrices. Be careful th ...

Premultiplymeans multiply on the left of each side. Matrices (Chapter 12) 327 From theDiscoveryyou should have found that ifAand ...

parallel (no solution) coincident (infinitely many solutions) unique solution 328 Matrices (Chapter 12) We can solve ½ 2 x+3y=4 ...

Matrices (Chapter 12) 329 b In matrix form, the system is μ 23 54 ¶μ x y ¶ = μ 4 17 ¶ which has the form AX=B. c Premultiplying ...

330 Matrices (Chapter 12) Review set 12A #endboxedheading 1 If A= μ 32 0 ¡ 1 ¶ and B= μ 10 ¡ 24 ¶ , find: a A+B b 3 A c ¡ 2 B d ...

Matrices (Chapter 12) 331 11 Solve using an inverse matrix: a ½ 3 x¡ 4 y=2 5 x+2y=¡ 1 b ½ 4 x¡y=5 2 x+3y=9 12 Suppose A=2A¡^1. a ...

332 Matrices (Chapter 12) 8 For A= μ 32 ¡ 11 ¶ , find: a detA b det (¡ 2 A) c det (A^2 ) 9 Solve using an inverse matrix: a ½ x+ ...

13 Introduction to differential calculus Contents: A Limits B Rates of change C The derivative function D Differentiation from f ...

334 Introduction to differential calculus (Chapter 13) Opening problem In a BASE jumping competition from the Petronas Towers in ...

Introduction to differential calculus (Chapter 13) 335 The concept of alimitis essential to differential calculus. We will see t ...

336 Introduction to differential calculus (Chapter 13) In practice we do not need to graph functions each time to determine limi ...

Introduction to differential calculus (Chapter 13) 337 Speedis a commonly used rate. It is the rate of change in distance per un ...

338 Introduction to differential calculus (Chapter 13) Theaveragespeed in the time interval 26 t 64 = distance travelled time ta ...

DEMO As B approaches A, the gradient of AB approaches orconvergesto. 2 A() 11 ,¡ y x f(x) = x¡¡ 2 O B,(x x )¡ 2 A() 11 ,¡ y x f( ...

340 Introduction to differential calculus (Chapter 13) EXERCISE 13B 1 Use the method inDiscovery 1to answer theOpening Problemon ...