1.3 Vector Equations

Question 1

column vector / vector

Answer 1

a matrix with only one column

Question 2

equal vectors

Answer 2

two vectors are equal if and only if their corresponding entries are equal

Question 3

scalar multiple of u by c

Answer 3

cu, obtained by multiplying each entry in u by c

Question 4

zero vector

Answer 4

vector whose entires are all zero and is denoted by 0

Question 5

linear combination

Answer 5

given vectors v1, v2, …, vn and scalars c1, c2, …, cn the vector y defined by y=c1v1 + … + cnvn is a linear combination of v1…vn with weights c1…cn

Question 6

subset

Answer 6

the set of all linear combination of v1…vp, denoted by Span{v1…vp}

Question 7

Span{v1…vp}

Answer 7

the collection of all vectors that can be written in the form c1v1+…+cpvp