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MATA23H3 (77)
Lecture

# Week 1 Lecture Notes.pdf

3 Pages
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Department
Mathematics
Course
MATA23H3
Professor
Kathleen Smith
Semester
Winter

Description
n Euclidean n{space, R , is de▯ned as R = f (x ;x 1 ▯▯2 ;x ) j xn2 R;ii= 1;2;▯▯▯ ;x g n { set of all n{tuples Eachn{tupleof realnumbers(R )can beviewedasapoint (x ;▯▯▯ ;x ) 1 n th or a vector [x 1▯▯▯ ;x ]n The i entry, x , ofithe vector is called the i component or i coordinate of the vector. A vector is in standard position if its tail is at the origin. If it starts at another point p, it is said to be translated to p. De▯nition: Let v = [v ;v ; ▯▯▯ ;v ] and w = [w ;w ; ▯▯▯ ;w ] be 1 2 n 1 2 n n vectors in R . The vectors are added and subtracted as follows: vector addition: v + w = [v + w ;v 1 w ; 1▯▯ 2v + w2] n n vector subtraction: v ▯ w = [v ▯ w ;v ▯ 1 ; ▯▯1 ;v2▯ w ]2 n n If ▯ is a scalar, the vector v is multiplied by ▯ as follows: scalar multiplication: ▯v = [▯v ;▯v ; ▯▯▯ ;▯v ]. 1 2 n Th
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