7. Matrices & transformations

Question 1

AB != BA

Answer 1

Matrix multiplication is not commutitive

Question 2

A(BC) = (AB)C

Answer 2

Matrix multiplication is associative

Question 3

You can only add matrices if…

Answer 3

they have the same m x n

Question 4

A(B + C) = AB + BC

Answer 4

It is distributive

Question 5

What is conformable?

Answer 5

M x N order can be multiplied by N x P order to make M x P

Question 6

A stretch parallel to x axis by scale factor k

Answer 6

K 0

0 1

Question 7

A stretch parallel to y axis by scale factor k

Answer 7

1 0

0 K

Question 8

An enlargement at O with scale factor K

Answer 8

K 0

0 K

Question 9

A rotation 90° anticlockwise about O

Answer 9

0 -1

1 0

Question 10

A rotation 90° clockwise about O
//270° anticlockwise

Answer 10

0 1

-1 0

Question 11

Leading diagonal rule matricies

Answer 11

Elements in the leading diagonal stay the same

Elements in the opposing diagonal switch signs

Question 12

A rotation of any angle anticlockwise

Answer 12

cosθ -sinθ

sinθ cosθ

Question 13

A reflection in the x axis

Answer 13

1 0

0 -1

Question 14

A reflection in the y axis

Answer 14

-1 0

0 1

Question 15

Multiplying by

A) Identity Matrix
B) 0/Null Matrix

Answer 15

A) Values stay the same

B) All values become 0

Question 16

Reflection in the line y = -x

Answer 16

0 -1

-1 0

Question 17

Shear

Answer 17

A transformation in which all the points are translated parallel to a particular line by a factor which is proportional to the distance of the point from a shear line

Question 18

Shear parallel to the x axis

Answer 18

1 K

0 1

Question 19

Shear parallel to the y axis

Answer 19

1 0

K 1

Question 20

Reflection in the yz plane (x = 0 plane)

Answer 20

-1 0 0
0 1 0
0 0 1

Question 21

Reflection xz plane (y = 0 plane)

Answer 21

1 0 0
0 -1 0
0 0 1

Question 22

Reflection xy plane (z= 0 plane)

Answer 22

1 0 0
0 1 0
0 0 -1

Question 23

Rotation of 180 about the z axis`

Answer 23

-1 0 0
0 -1 0
0 0 1

Question 24

Invarient Point

Answer 24

A point which is mapped to itself by the transformation

Question 25

How to find lines of invarient points

Answer 25

1. Multiply the matrix by XY and make it equal to XY
2. Multiply into two different equations
3. If (ax + by = x) = (cx + dy = y) then all the points along the ax + by = x are invariant points

Question 26

Determinant

Answer 26

ad - bc

Question 27

If the matix’s determinant is 0 then…

Answer 27

the matrix is singular and has no inverse

Question 28

Inverse of a 2x2 matrix

Answer 28

1/|M|
(d -b)
(-c a)

Question 29

AA^-1

Answer 29

Is equal to I

Question 30

(AB)^-1

Answer 30

A^-1 B^-1

Question 31

A rotation 180° anticlockwise about O

Answer 31

-1 0

0 -1

Question 32

`Reflection on the line y = x

Answer 32

0 1

1 0

Question 33

Applying transformations

Answer 33

if C represents A transformed by B

C = BA

Question 34

Determinant for rotations, reflections and enlargements

Answer 34

Rotation: detM = 1
Reflection: detM = -1
Enlargement: detM = k²

Question 35

Reflection in the line y = (tanθ)x

Answer 35

cos 2θ sin 2θ

sin 2θ -cos 2θ