Matrices

Question 1

What is the order of the following matrices ?

Answer 1

Number of rows by numbers of columns
y by x

Question 2

What does it mean for matrices to be “non conformable”?

Answer 2

This means that they matrices do not have the exact same order. For example

Question 3

What does associative mean?

Answer 3

It means that despite the order/ grouping of numbers, the answers will be the same.

Question 4

What does it mean for something to be commutative ?

Answer 4

Question 5

What are the general steps to carrying out matrices multiplication?

Answer 5

1. write out the order of both matrices
2. see if compatible, if they are write order of answer matrix
3. start with first element (1x1) first row by first colum
4. multiply each pair of numbers and add up the answers
5. then go onto next element (1x2) first row by second column
6. multiply each pair and add up numbers

Question 6

Multiply

Answer 6

Question 7

Multiply (find FE)

Answer 7

Question 8

Is matrix muliplication commutative or associative?

Answer 8

• not commutative
  as order within which multiplied does matter
• is associative

Question 9

what is the original point/shape and the transformed point/shape reffered to ?

Answer 9

• orginal= object
• transformed= image

Question 10

what is a transformation?

Answer 10

the mapping of an object onto a image

Question 11

how do you find the transformation representated by a given matrix?

Answer 11

1. split up the identity matrix into points (unit vectors)
2. see how they have been transformed by ploting the points on a graph

Question 12

Describe the transformation of the matrix

Answer 12

Question 13

Answer 13

Question 14

What is the transformation matrix for any angle theta anti-clockwise. ?

Answer 14

Question 15

What is the matrix transformation for any clockwise rotation by angle theta?

Answer 15

Question 16

Describe the transformation by the matrix

Question 17

Describe the transformation by the matrix

Answer 17

Question 18

What are shears?

Answer 18

The base stays rooted and the rest shifts and becomes parallel. The area of original shape is the same to the shear.

Question 19

What are the 2 different types of shears?

Answer 19

Question 20

Successive transformations

Answer 20

Question 21

3D matrices

Answer 21

Question 22

Describe the Transformation under matrix

Question 23

Describe the Transformation under matrix

Answer 23

Question 24

Describe the transformation

Question 25

What are invariant points?

Answer 25

Points that do not change after a transformation. The origin will always be an invariant point

Question 26

What are invariant lines?

Answer 26

A line of points that MAY be invariant or points that remain upon that line after a transformation

Question 27

Answer 27

Question 28

More proof by induction matrices

Answer 28

Question 29

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Question 30

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Question 31

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Question 32

Describe the 3D planes

Answer 32

Question 33

What are the components of an algorithm?

Answer 33

* finite number of steps * unambigious steps * deterministic

Question 34

What is complexity ?

Answer 34

* Size in relation to run time (efficiency ) * measure of which one is faster

Question 35

Perform a quick sort algorithm to sort it into ascending order

Answer 35

**values less than or equal to go to the left of pivot**

Question 36

what is * first fit * first fit decreasing * full bin

Answer 36

* FF: putting the numbers using given order in question * FFD: ordering the list into descending order - biggest first * FB: using brain for optimal solution

Question 37

what does heuristic mean?

Answer 37

* a method that finds the solution efficently, but with no gurante that this solution is optimal * important when classical methods fail, only way to find is exhauting all solutions

Question 38

how can the efficency of different packing methods be tested?

Answer 38

counting the number of comparisions needed in worst case

Question 39

what is the complexit of the first fit and first fit decreasing algorithm , in the worst case?

Answer 39

o (n sqaured)

Question 40

what is the complexity of the quick sort algorithm , in the worst case?

Answer 40

O (n squared)

Question 41

What is big O notation?

Answer 41

Question 42

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Question 43

Use quick sort to sort the following numbers in descending order

Question 44

Use quick sort to sort the following numbers in descending order

Answer 44

Question 45

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Question 46

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Question 47

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Question 48

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Question 49

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Question 50

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Question 51

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Question 52

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