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A Level Further maths > Matrices > Flashcards

Matrices Flashcards

1
Q

What is the order of the following matrices ?

A

Number of rows by numbers of columns
y by x

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2
Q

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

A

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

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3
Q

What does associative mean?

A

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

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4
Q

What does it mean for something to be commutative ?

A
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5
Q

What are the general steps to carrying out matrices multiplication?

A
  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
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6
Q

Multiply

A
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7
Q

Multiply (find FE)

A
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8
Q

Is matrix muliplication commutative or associative?

A
  • not commutative
    as order within which multiplied does matter
  • is associative
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9
Q

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

A
  • orginal= object
  • transformed= image
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10
Q

what is a transformation?

A

the mapping of an object onto a image

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11
Q

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

A
  1. split up the identity matrix into points (unit vectors)
  2. see how they have been transformed by ploting the points on a graph
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12
Q

Describe the transformation of the matrix

A
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13
Q
A
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14
Q

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

A
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15
Q

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

A
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16
Q

Describe the transformation by the matrix

A
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17
Q

Describe the transformation by the matrix

A
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18
Q

What are shears?

A

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

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19
Q

What are the 2 different types of shears?

A
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20
Q

Successive transformations

A
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21
Q

3D matrices

A
22
Q

Describe the Transformation under matrix

A
23
Q

Describe the Transformation under matrix

A
24
Q

Describe the transformation

A
25
Q

What are invariant points?

A

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

26
Q

What are invariant lines?

A

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

27
Q
A
28
Q

More proof by induction matrices

A
29
Q
A
30
Q
A
31
Q
A
32
Q

Describe the 3D planes

A
33
Q

What are the components of an algorithm?

A
  • finite number of steps
  • unambigious steps
  • deterministic
34
Q

What is complexity ?

A
  • Size in relation to run time (efficiency )
  • measure of which one is faster
35
Q

Perform a quick sort algorithm to sort it into ascending order

A

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

36
Q

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

A
  • FF: putting the numbers using given order in question
  • FFD: ordering the list into descending order - biggest first
  • FB: using brain for optimal solution
37
Q

what does heuristic mean?

A
  • 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
38
Q

how can the efficency of different packing methods be tested?

A

counting the number of comparisions needed in worst case

39
Q

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

A

o (n sqaured)

40
Q

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

A

O (n squared)

41
Q

What is big O notation?

A
42
Q
A
43
Q

Use quick sort to sort the following numbers in descending order

A
44
Q

Use quick sort to sort the following numbers in descending order

A
45
Q
A
46
Q
A
47
Q
A
48
Q
A
49
Q
A
50
Q
A
51
Q
A
52
Q
A

A Level Further maths (10 decks)

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