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

Answer 20

Question 21

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

Answer 21

Question 22

Answer 22

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

Answer 29

Question 30

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

Answer 30

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

Question 31

Answer 31

Question 32

Answer 32

Question 33

what is the wording when describing rotaions in 3D?

Answer 33

rotation in the x axis

not plane

Question 34

What is an invariant point?

Answer 34

Question 35

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Question 36

Answer 36

Question 37

What are invariant lines?

Answer 37

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

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Question 44

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

Answer 44

(A^k)(A)

Question 45

what is the determinant of a matrix?

for a 2x2

Answer 45

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

Question 46

what is the determinant of a 3x3 matrix?

Answer 46

the volume scale factor

Question 47

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

Answer 47

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 48

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

2x2

Answer 48

becomes A’B’C’D’ anticlockwise

Question 49

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

3x3

Answer 49

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

Question 50

what is det(MN)?

Answer 50

det(M) x det(N)

Question 51

Describing shears
What is the general form for describing shears?

Answer 51

Question 52

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Question 53

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Question 54

Answer 54

Don’t use ans key in calculator when using matrices

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

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Question 62

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

Answer 62

The reciprocal

Question 63

Answer 63