Chapter 1

Question 1

R2

Answer 1

Two dimensional space

Question 2

R3

Answer 2

3 dimensional space

Question 3

N tupple

Answer 3

An ordered list of n numbers enclosed in brackets

Question 4

Coordinates

Answer 4

The n tupple that the position of a point

Question 5

Scalar

Answer 5

Object that can be described entirely by a number

Question 6

Vector

Answer 6

An object described by its number value(magnitude) and a direction

Question 7

Components

Answer 7

Each item of a vector

Question 8

Trivial solution

Answer 8

The solution that consists of the zero vector

Question 9

Unit vector

Answer 9

A vector of length 1

Question 10

Standard basis vector is r2 and r3

Answer 10

R2- {e1=(1,0), e2=(0,1)}

R3- {e1=(1,0,0), e2=(0,1,0), e3= (0,0,1)}

Question 11

What is the trivial solution?

Answer 11

A solution that consists of only the zero vector

Question 12

What is a unit vector?

Answer 12

A vector of length 1

Question 13

What is span?

Answer 13

The set of all linear combinations in a set of vectors- doesnt need to be Linear independent

Question 14

What is Linear independence?

Answer 14

A non empty set of vectors whos scalars satisfy

C1V1 + C2V2 + C3V3…. + CNVN= 0

Question 15

What is linear dependence?

Answer 15

When the function has a C scalar that is not 0

Question 16

What is a basis?

Answer 16

A set of vectors is called a basis when the set is a span and the set is LI