Lecture 1.pdf

# Introduction example given a 1 2 and b 1 3 find the

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Introduction Example Given A = (1 , 2) and B = ( - 1 , 3), find the vectors -→ AB = h- 1 - 1 , 3 - 2 i = h- 2 , 1 i 10/20
Introduction Example Given A = (1 , 2) and B = ( - 1 , 3), find the vectors -→ AB = h- 1 - 1 , 3 - 2 i = h- 2 , 1 i -→ BA 10/20
Introduction Example Given A = (1 , 2) and B = ( - 1 , 3), find the vectors -→ AB = h- 1 - 1 , 3 - 2 i = h- 2 , 1 i -→ BA = h 1 - ( - 1) , 2 - 3 i 10/20
Introduction Example Given A = (1 , 2) and B = ( - 1 , 3), find the vectors -→ AB = h- 1 - 1 , 3 - 2 i = h- 2 , 1 i -→ BA = h 1 - ( - 1) , 2 - 3 i = h 2 , - 1 i 10/20
Introduction Example Given A = (1 , 2) and B = ( - 1 , 3), find the vectors -→ AB = h- 1 - 1 , 3 - 2 i = h- 2 , 1 i -→ BA = h 1 - ( - 1) , 2 - 3 i = h 2 , - 1 i 10/20
Introduction Notation 11/20
Introduction Notation h a , b , c i denotes the vector in R 3 whose starting point is (0 , 0 , 0) and ending point is ( a , b , c ). 11/20
Introduction Notation h a , b , c i denotes the vector in R 3 whose starting point is (0 , 0 , 0) and ending point is ( a , b , c ). Likewise, h a , b i denotes the vector in R 2 whose starting point is (0 , 0) and ending point is ( a , b ). 11/20
Introduction Notation 12/20
Introduction Notation Sometimes it is convenient to denote vectors as columns: 12/20
Introduction Notation Sometimes it is convenient to denote vectors as columns: -→ v = h a , b , c i = a b c = a b c T 12/20
Introduction Operations with vectors 13/20
Introduction Operations with vectors Addition and Subtraction: 13/20
Introduction Operations with vectors Addition and Subtraction: h a 1 , b 1 , c 1 i ± h a 2 , b 2 , c 2 i 13/20
Introduction Operations with vectors Addition and Subtraction: h a 1 , b 1 , c 1 i ± h a 2 , b 2 , c 2 i = h a 1 ± a 2 , b 1 ± b 2 , c 1 ± c 2 i 13/20
Introduction Operations with vectors Addition and Subtraction: h a 1 , b 1 , c 1 i ± h a 2 , b 2 , c 2 i = h a 1 ± a 2 , b 1 ± b 2 , c 1 ± c 2 i Multiplication by scalar: 13/20
Introduction Operations with vectors Addition and Subtraction: h a 1 , b 1 , c 1 i ± h a 2 , b 2 , c 2 i = h a 1 ± a 2 , b 1 ± b 2 , c 1 ± c 2 i Multiplication by scalar: k · h a , b , c i 13/20
Introduction Operations with vectors Addition and Subtraction: h a 1 , b 1 , c 1 i ± h a 2 , b 2 , c 2 i = h a 1 ± a 2 , b 1 ± b 2 , c 1 ± c 2 i Multiplication by scalar: k · h a , b , c i = h ka , kb , kc i 13/20
Introduction Length, magnitude, or norm 14/20
Introduction Length, magnitude, or norm Given a vector -→ v = h a , b , c i we denote its length (or magnitude, or norm) by 14/20

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