Vector in R space.
T uple = A tuple is a finite ordered list of elements sequence of n-elements where n is a non-negative integer. Set of n-tuples of Real Numbers => R n Note: O-tuple = Empty space Eg. (0,0,0,0...........) A particular n tuple in R n U = ( a1,a2,a3,..................an ) is called a point or vector. [ where, (a1,a2,a3,.............an) is called Scalar & U is called Vector. ] or, U = [a¡] ,where i is called as components/entries/co-ordinates/elements. Note: Elements of R = S calar . 1.) Two vectors U & V are equal i.e U=V if they have same number of components and the corresponding components are equal . e.g. U =[a1,a2,a3] V =[b1,b2,b3] If U =V then a1=b1 , a2=b2 , a3=b3 2.) U=[0,0,0..........0] This is Zero vector and is denoted as Bold 0 (𝐨). Example : Q ) Identify the space : a) (2,-5) -> R 2 b) (3,4,5) -> R^3 Q ) Find x,y,z such that (x-y , x+y , Z-