Matrices (pt2) Flashcards

1
Q

what are the two function of matrices?

A
  • representing linear transformations (rotation, reflection, enlargments)
  • solving simultaneous equations
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2
Q

what is the dimension of a matrix?

A
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3
Q

what is associativity?

A
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4
Q

what is commutativity?

A
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5
Q

what is an identity matrix?

A
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6
Q

what is a square matrix?

A

only square matrices can be rasied to a power

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7
Q

is matrix multiplication assoiciative?

A

Yup

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8
Q

Is matrix multiplication commutative?

A

Nope

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9
Q

how do you enter matrices on calculator?

A
  1. menu-1
  2. MATH
  3. MAT/VCM
  4. select dimention of matrix
    OR to save matrices as variables
  5. MAT/VCM
  6. (to retrieve) , OPTN
  7. MAT/VCM
  8. Mat
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10
Q
A
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11
Q

What is the general form of linear functions/ transformations?

A

Matrix, position vector

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12
Q
A
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13
Q

What is the notation used to denote?

A

The image

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14
Q

Using identity matrix to figure out transformations

A
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15
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16
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17
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18
Q
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19
Q

Find the angle and direction of rotation in each case

A
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20
Q
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21
Q

What is the difference between a stretch and a shear, and their general form :

A
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22
Q
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23
Q

What is the Shear Factor?

A

distance moved by a point divided by it’s perpendicular distance from the fixed line.
fixed line of shear is a line of invariant points

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24
Q
A
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Reflect in the plane z=0
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What are the matrices for rotation about the x, y and z axis on an angle of θ?
| notice how the sin is only switched for the y axis rotations
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what is the wording when describing rotaions in 3D?
rotation in the x **axis** | not plane
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What is an invariant point?
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What are invariant lines?
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What is the formula for A^k+1 in terms of A?
(A^k)(A)
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what is the determinant of a matrix? | for a 2x2
gives the area scale factor of the transformation * ad-bc
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what is the determinant of a 3x3 matrix?
the volume scale factor
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what does it mean when the determinant of the matrix = 0 * 2x2 * 3x3
if det M= 0 then singular matrix if det M ≠ 0 then non- singular * for a 2x2 transforms them onto a line * for a 3x3 Geometrically, it means that the three vectors represented by the rows or columns of the matrix lie in a plane rather than filling 3D space.
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what would a negative determinant do to the image ABCD labelled clockwise | 2x2
becomes A'B'C'D' anticlockwise
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what would a negative determinant do to the image ABCD labelled clockwise when seen from point S | 3x3
becomes A'B'C'D' anticlockwise when seen from point S'
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what is det(**MN**)?
det(**M**) x det(**N**)
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Describing shears What is the general form for describing shears?
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Don’t use ans key in calculator when using matrices
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What is the determinant of an inverse matrix in respect to the determinant of the original matrix?
The reciprocal
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