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Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices MAT188H1F Lec0106 Burbulla Chapter 1 Lecture Notes Fall 2010 Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Good and Bad Notation, and Some General Advice Examples Appendix 2: Induction Examples Chapter 1: Linear Equations and Matrices 1.1 Matrices 1.2 Linear Equations 1.3 Homogeneous Systems 1.4 Matrix Multiplicaton 1.5 Matrix Inverses 1.6 Elementary Matrices Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla

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Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Notation Mathematics has its own set of symbols. If you use them, you must use them correctly. You will lose marks on tests or exams if your notation is incorrect. Following are some examples of common errors. Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Example 1 Suppose you are differentiating the function y = x 2 . If you write y = x 2 = 2 x it is incorrect, even though most people would know what you are doing. Of course, you should write y = x 2 y = 2 x Or you could simply write dx 2 dx = 2 x . Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla
Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Example 2 Don’t confuse implication ( ) with equality ( = ) . The symbol is a logical connective and means If . . . then . . . . For example, if y = x 2 , then y = 2 x , can be written as y = x 2 y = 2 x . But writing something like ax 2 + bx + c 0 x - b ± b 2 - 4 ac 2 a is abuse of notation. Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Example 3 The expressions 0 0 , , 0 0 , 0 · ∞ , 1 , 0 and ∞ - ∞ are indeterminate. When evaluating limits of this type, which may or may not exist, don’t equate the limit to one of the above expressions. For example, writing lim x 1 x 3 - 1 x 2 - 1 = 0 0 is incorrect; the limit is actually equal to 3 2 . You can say the limit is of the form 0 0 ; or that when x = 1 , x 3 - 1 x 2 - 1 = 1 - 1 1 - 1 = 0 0 , which is indeterminate. Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla

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Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Example 4 When reducing a matrix, don’t put equal ( = ) signs between matrices which aren’t equal: 1 3 - 2 - 2 3 1 1 2 - 1 = 1 3 - 2 0 9 - 3 0 - 1 1 is incorrect. Instead, use an arrow ( ) between row equivalent matrices: 1 3 - 2 - 2 3 1 1 2 - 1 1 3 - 2 0 9 - 3 0 - 1 1 .
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