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A Level Further Maths > Core Pure - Matrices + Linear Transformations > Flashcards

Core Pure - Matrices + Linear Transformations Flashcards

1
Q

What is a square vector?

A

A matrix when the number of rows and columns are the same

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2
Q

What is an identity matrix?

A

A square matrix with 1’s along the principal diagonal and the rest of the elements as 0

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3
Q

How do you find the determinant of a 2x2 matrix?

A
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4
Q

How do you find the determinant of a 3x3 matrix?

A
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5
Q

What is a singular matrix?

A

A matrix where Det M = 0

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6
Q

How do you find the inverse of a 2x2 matrix?

A
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7
Q

What is the property of an inverse matrix?

A

MM⁻¹ = I

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8
Q

How do you find the inverse of a 3x3 matrix?

A
  1. Find the determinant of A, Det A
  2. Form the matrix of minors, M
  3. From the matrix of minors, form the matrix of cofactors, C
  4. Find the Transpose of the matrix of cofactors, Cᵀ
  5. A⁻¹ = (1/DetA) Cᵀ
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9
Q

What is the transpose of a matrix?

A

The reflection across the main diagonal

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10
Q

If the determinant of a matrix corresponding to 3 simultaneous equations is singular, is it consistent or inconsistent and how many solutions does it have?

A

If Det A = 0, the simulatanous equations may:
* Be consistnent and have infinite solutions
* Or be inconsistent and no solutions

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11
Q

If the determinant of a matrix corresponding to 3 simultaneous equations is non-singular, is it consistent or inconsistent and how many solutions does it have?

A

Is is consistant and has 1 unique solution

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12
Q

What is the gemoetrical representation of a matrix corresponding to 3 simultaneous equations when the determinant does NOT equal 0?

A
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13
Q

What is the gemoetrical representation of a matrix corresponding to 3 simultaneous equations when it is singular and has infinite solutions?

A
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14
Q

What is the gemoetrical representation of a matrix corresponding to 3 simultaneous equations when it is singular and has no solutions?

A
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15
Q

How do you determine whether 3 simultaneous equations with det A = 0 are consistent or inconsistent?

A

Form 2 equations from the 3 equatiosn (set 1 equal to x,y or z and substitute in to other 2), of the 2 formed equations are multiples of each other, it is consistent, if they are not multiples, they are inconsistent

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16
Q

How do you determine whether 3 simultaneous equations are represented gemoetrically by a prism or 2 or more planes being parallel?

A
  • Prism if at least 2 of the original equations are not mulriples of each other
  • Parallel if at least 2 of the original equations are multiples of each other
17
Q

What is a linear transformation?

A

A transformation where the origin is unmoved

18
Q

How do you transforma. point using matrices?

A

Ma = a’

(a’ = a image)

19
Q

How do you determine the 2x2 matrix for a transformation?

A

Using a unit square

20
Q

What is the rotation matrix for a 2d graph?

A
21
Q

What is the equation for the image area?

A

Image area = Det M x Object acrea

22
Q

What is the enlargement scale factor?

A

root(determinant)

23
Q

What linear transformation does this matrix represent?

A

Enlargement, centre 0, scale factor a

24
Q

What linear transformation does this matrix represent?

A

Shear transfmormation, centre 0, scale factor a parallel to the x axis and scale factor b parallel to the y axis

25
Q

What is the matrix for matrix A followed by matrix B?

A

BA

26
Q

What is an invariant point?

A

A point which does not move under the transformation

27
Q

What is an invariant line?

A

a line where any point on the line is mapped to another point which is also on the line. Howevever, individual points are not invariant

28
Q

What matrix is a reflection in the plane x=0 represented by?

A
29
Q

What matrix is a reflection in the plane y=0 represented by?

A
30
Q

What matrix is a reflection in the plane z=0 represented by?

A
31
Q

What matrix represents a rotation about the x axis?

A
32
Q

What matrix represents a rotation about the y axis?

A
33
Q

What matrix represents a rotation about the z axis?

A
34
Q

What is the plane x = 0?

A

The y-z plane

35
Q

What is the plane y=0?

A

the x-z plane

36
Q

What is the plane z=0?

A

the x-y plane

A Level Further Maths (14 decks)

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