Week 1

Question 1

What is LINEAR ALGEBRA (LA)?

Answer 1

The study of VECTOR SPACES and LINEAR TRANSFORMATIONS between them.

Question 2

What are VECTOR SPACES?

Answer 2

A set of mathematical objects that can be added together and scaled (multiplied by a number)

Question 3

What is a LINEAR TRANSFORMATION?

Answer 3

A special map that preserves addition and scaling

Question 4

What does the symbol “ ℝ “ stand for?

Answer 4

ℝ means “THE SET OF REAL NUMBERS”

Question 5

What does the symbol “ ∈ “ stand for?

Answer 5

∈ means “IS AN ELEMENT OF”

Question 6

What do these mean?

	i•         1 ∈ ℝ
	ii•       -4 ∈ ℝ
	iii•      -5/7 ∈ ℝ
	iv•     √2 ∈ ℝ
	 v•      π ∈ ℝ

Answer 6

i• 1 ∈ ℝ ► “1 is an element of the set of real #s”
ii• -4 ∈ ℝ ► “-4 is an element of the set of real #s”
iii• -5/7 ∈ ℝ ► “-5/7 is an element of the set of real #s” iv• √2 ∈ ℝ ► “√2 is an element of the set of real #s”
v• π ∈ ℝ ► “π is in the set of real numbers”

Question 7

**

What are SCALARS?

Answer 7

a quantity specified by a single number

denoted by plain letters such as α, β , ….

Question 8

What types of symbols are used to denote SCALARS?

Answer 8

scalars are denoted by PLAIN LETTERS such as α, β , ….

Question 9

Supposing P & Q are statements that can either be True or False. Translate what these statements mean:

i•           P => Q
ii•          P <= Q
iii•         P <=> Q

Answer 9

i• P => Q ► “If P then Q” or “P implies Q”
ii• P <= Q ► “P if Q” or “Q implies P”
iii• P <=> Q ► “P if and only if Q” i.e. P & Q are equivalent

Question 10

What is a VECTOR?

Answer 10

Geometrically, a vector is a DIRECTIONAL LINE SEGMENT. A vector is a quantity that is characterised by its MAGNITUDE (length) and DIRECTION.

Question 11

What are the characteristics of a VECTOR?

Answer 11

MAGNITUDE

DIRECTION

Question 12

What do NOT CHARACTERISE VECTORS?

Answer 12

The LOCATION of the vector on the plane

Question 13

List 3 examples of SCALAR quantities

Answer 13

Distance (e.g 60 km)
Speed (e.g. 60 km/hr)
Mass (e.g. 60 kg)

Question 14

List 3 examples of VECTOR quantities

Answer 14

Displacement (e.g. 60km NORTH EAST)
Velocity (e.g. 60km/hr NORTH EAST)
Acceleration (e.g. 60km/hr^2 SOUTH)
Weight (force due to gravity; 900Newtons)