Vectors and matrices

Question 1

What is the term when the order of multiplication doesn’t matter

Answer 1

Commutative

Question 2

What does the dot product end in?

Answer 2

A scalar number

Question 3

What is the commuatative property?

Answer 3

The order of multiplication doesn’t matter

Question 4

What is the distributative property?

Answer 4

You can multiply something outside of a bracket to the components inside

Question 5

Are vectors distributive?

Answer 5

Yes

Question 6

What is it called when you use dot product and multiple a vector over parenteses?

Answer 6

Distributive

Question 7

What is associative?

Answer 7

The grouping of multiplication doesn’t matter

Question 8

What is the difference between commutative, distributive and associative?

Answer 8

Commutative - the order of multiplication doesn’t matter
Distributive - you can multiply something outside of the bracket to the inside components
Associative - the grouping of multiplication doesn’t matter

Question 9

Whats the notation for a vector?

Answer 9

lower case with an arrow above it

Question 10

What is R2

Answer 10

Ordered 2 tupes where all the vlaues are real numbers

Question 11

What is standard position?

Answer 11

Origin

Question 12

What is the relationship between x-y and y - x

Answer 12

The same magnitude but opposite directions

Question 13

How do you denote a unit vector?

Answer 13

A hat

Question 14

What is a hat and arrow for?

Answer 14

Hat is unit vector

Arrow is a normal vector

Question 15

What are position vectors?

Answer 15

Tehy are co-ordinates i.e. they start at the origin

Question 16

What is the magnitude of a vector?

Answer 16

It’s the length of the line

Question 17

How do you measure the magnitude of a vector?

Answer 17

Create triangles and use pythagorus

Question 18

How do you denomate the magniude of a vector?

Answer 18

|| a with arrow ||

Question 19

How do you find a unit vector with a given direction?

Answer 19

Divide by the magnitude of the vector (so that the magnitude is 1)

Question 20

How do you represent a line? Where the line goes through the origin?

Answer 20

V = [2 1]

S = { c v | E R}

Set where scalar of the vector v where the scalar is a real number

Question 21

How do you get the vector between 2 position vectors?

Answer 21

Subtract one from the other

Question 22

Does the order matter when working out the vector between 2 position vectors

Answer 22

No

Question 23

How do you document a line that does not go through the origin?

Answer 23

S = { x + c v | c E R}

Question 24

How do you document a line that does not go through the origin and is given by 2 position vectors?

Answer 24

S = {a + c ( b - a) | c E R}

Question 25

True or false: can you reach any point on a 2d with linear combinations?

Answer 25

True

Question 26

What is linear independence?

Answer 26

Vectors that cannot be expressed by the other ones

Question 27

What do you have to have to represent any point in R2?

Answer 27

Two linerally indepednet vectors

Question 28

How do you prove that a set of vectors are lineally indepednet?

Answer 28

If you have any non zero value scalar where the vectors can be combined to be [0 0]

Question 29

How do you get the modulus of a vector?

Answer 29

Dot product of itself square rooted

Question 30

What is r.r?

Answer 30

r.r = ∥r∥2

Question 31

What is r.s?

Answer 31

r.s = ∥r∥∥s∥ cos θ

Question 32

What does it mean when r.s is zero?

Answer 32

They are orthogonal

Question 33

What does it mean when r.s is negative?

Answer 33

They are going in opposite directions

Question 34

What does it mean when r.s is positive?

Answer 34

They are going in the same direction

Question 35

What is the scalar projection?

Answer 35

Projection The component of a vector a that is in the same direction as of vector b (Hence projection is a vector) Length of the projection does not depend on the length(magnitude) of b. See the image below

Question 36

What is the forumula for scalar projection?

Answer 36

scalar projection: r.s _ ∥r∥

Question 37

What is the vector projection?

Answer 37

The sclar projecttion times by a unit vector in the direction of r

Question 38

What is the fomula for vector projection?

Answer 38

r.s _ r.r x r

Question 39

How do you change the basis in new orthogonal vectors?

Answer 39

For R in b1 and b2: r. b1 / b1.b1 r. b2 / b2.b2

Question 40

What is basis?

Answer 40

Basis is a set of n vectors that are linearly independent and span the space

Question 41

What do basis vector not have to be?

Answer 41

unit vectors or orthogonal

Question 42

What matrix changes nothing?

Answer 42

The identity matrix 1 0 0 1

Question 43

What does this matrix do? 0 1 1. 0

Answer 43

Mirror at 45 degrees

Question 44

What does this matrix do? 0 -1 -1 0

Answer 44

Mirror at 320 degrees

Question 45

What does this matrix do? -1 0 0 1

Answer 45

Mirror along the vertical axis

Question 46

What does this matrix do? 1 0 0 - 1

Answer 46

Mirror along the horizontal axis

Question 47

What does this matrix do? 0 1 1 0

Answer 47

Rotate by 90 degrees anticlockwise

Question 48

What is the general equation for a rotation?

Answer 48

cos theta sin theta | -sin theta cos theta

Question 49

Are matrices commutative?

Answer 49

No

Question 50

Are matrices associative?

Answer 50

Yes

Question 51

What is the determinant?

Answer 51

The area in space that has got bigger by a factor

Question 52

How do you denote the determinant?

Answer 52

| A |

Question 53

What is | A | ?

Answer 53

ad - bc where A a b c d

Question 54

How do you find the inverse of a 2 x 2 matrix? a b c d

Answer 54

d -b | c -a

Question 55

What is the determinant for 1 2 1 2

Answer 55

0 - it's on a line