Lab 2 Notes.pdf - MA122 Lab Report 2 Notes Vectors in Rn 1 When n = 2 x T where(x y can be thought of as the point on the xy-axes(i.e two dimensional =
MA122 Lab Report 2 NotesVectors inRn:1. Whenn= 2 :Denoted by°!a=a=°xy±=²xy³Twhere(x; y)can be thought of as the point on thexy-axes (i.e. two dimensional)and the vector is an arrow from the origin to the point.2. Whenn= 3 :Denoted by°!a=a=24xyz35=x°!i+y°!j+z°!kwhere(x; y; z)can be thought of as the point on thexyz-axes (i.e. threedimensional) and the vector is an arrow from the origin to the point.Note:°!i=2410035,°!j=2401035;and°!k=2400135are called the standard basis forR3:3. Whenn >3 :Denoted by°!a=26664x1x2...xn37775which can no longer be visualized but is still an arrow from the origin to a "point".Vector Calculations:Given°!a=a=²x1x2± ± ±xn³T,°!b=b=²y1y2± ± ±yn³T;andk2R;the following properties hold whenn= 2;3; ::::1.Addition:~a+~b=²x1± ± ±xn³T+²y1± ± ±yn³T=²x1+y1± ± ±xn+yn³TGeometrically, it you draw a parallelogram with~aand~bbeing adjacent sides, then~a+~bis the vectorfrom the origin to the vertex of the parallelogramopposite the origin.