Matrices (pt2)

Question 1

what are the two function of matrices?

Answer 1

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

Question 2

what is the dimension of a matrix?

Answer 2

Question 3

what is associativity?

Answer 3

Question 4

what is commutativity?

Answer 4

Question 5

what is an identity matrix?

Answer 5

Question 6

what is a square matrix?

Answer 6

only square matrices can be rasied to a power

Question 7

is matrix multiplication assoiciative?

Answer 7

Yup

Question 8

Is matrix multiplication commutative?

Answer 8

Nope

Question 9

how do you enter matrices on calculator?

Answer 9

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

Question 10

Answer 10

Question 11

What is the general form of linear functions/ transformations?

Answer 11

Matrix, position vector

Question 12

Answer 12

Question 13

What is the notation used to denote?

Answer 13

The image

Question 14

Using identity matrix to figure out transformations

Answer 14

Question 15

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Question 16

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Question 17

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Question 18

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Question 19

Find the angle and direction of rotation in each case

Answer 19

Question 20

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Question 21

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

Answer 21

Question 22

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Question 23

What is the Shear Factor?

Answer 23

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

Question 24

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Question 25

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Question 26

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Question 27

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Question 28

Reflect in the plane z=0

Answer 28

Question 29

What are the matrices for rotation about the x, y and z axis on an angle of θ?

Answer 29

| notice how the sin is only switched for the y axis rotations

Question 30

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Question 31

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Question 32

what is the wording when describing rotaions in 3D?

Answer 32

rotation in the x **axis** | not plane

Question 33

What is an invariant point?

Answer 33

Question 34

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Question 35

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Question 36

What are invariant lines?

Answer 36

Question 37

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Question 38

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Question 39

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Question 40

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Question 41

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Question 42

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Question 43

What is the formula for A^k+1 in terms of A?

Answer 43

(A^k)(A)

Question 44

what is the determinant of a matrix? | for a 2x2

Answer 44

gives the area scale factor of the transformation * ad-bc

Question 45

what is the determinant of a 3x3 matrix?

Answer 45

the volume scale factor

Question 46

what does it mean when the determinant of the matrix = 0 * 2x2 * 3x3

Answer 46

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.

Question 47

what would a negative determinant do to the image ABCD labelled clockwise | 2x2

Answer 47

becomes A'B'C'D' anticlockwise

Question 48

what would a negative determinant do to the image ABCD labelled clockwise when seen from point S | 3x3

Answer 48

becomes A'B'C'D' anticlockwise when seen from point S'

Question 49

what is det(**MN**)?

Answer 49

det(**M**) x det(**N**)

Question 50

Describing shears What is the general form for describing shears?

Answer 50

Question 51

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Question 52

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Question 53

Answer 53

Don’t use ans key in calculator when using matrices

Question 54

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Question 55

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Question 56

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Question 57

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Question 58

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Question 59

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Question 60

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Question 61

What is the determinant of an inverse matrix in respect to the determinant of the original matrix?

Answer 61

The reciprocal

Question 62

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Question 63

Answer 63