Matrix Transformations

Question 1

What is the 2x2 identity matrix?

Answer 1

[1 0]
[0 1]

Question 2

What is the 3x3 identity matrix?

Answer 2

[1 0 0]
[0 1 0]
[0 0 1]

Question 3

What matrix is for a reflection in the line y = 0?

Answer 3

[1 0]
[0 -1]

Question 4

What matrix is for a reflection in the line x = 0?

Answer 4

[-1 0]
[0 1]

Question 5

What matrix is for a reflection in the line y = x?

Answer 5

[0 1]
[1 0]

Question 6

What matrix is for a reflection in the line y = -x?

Answer 6

[0 -1]
[-1 0]

Question 7

What matrix is for a rotation of 90° clockwise?

Answer 7

[0 1]
[-1 0]

Question 8

What matrix is for a rotation of 90° anticlockwise?

Answer 8

[0 -1]
[1 0]

Question 9

What matrix is for a rotation of 180°?

Answer 9

[-1 0]
[0 -1]

Question 10

What matrix is for an enlargement with a scale factor of k?

Answer 10

[K 0]
[0 K]

Question 11

What is the matrix for a stretch with a scale factor of k parallel to the x axis?

Answer 11

[K 0]
[0 1]

Question 12

What is the matrix for a stretch with a scale factor of k parallel to the y axis?

Answer 12

[1 0]
[0 K]

Question 13

What is the matrix for a reflection in the x plane?

Answer 13

[-1 0 0]
[0 1 0]
[0 0 1]

Question 14

What is the matrix for a reflection in the y plane?

Answer 14

[1 0 0]
[0 -1 0]
[0 0 1]

Question 15

What is the matrix for a reflection in the z plane?

Answer 15

[1 0 0]
[0 1 0]
[0 0 -1]

Question 16

What is the 3x3 matrix for a rotation of θ° anticlockwise about the x axis?

Answer 16

[1 0 0]
[0 cosθ -sinθ]
[0 sinθ cosθ]

Question 17

What is the 3x3 matrix for a rotation of θ° anticlockwise about the y axis?

Answer 17

[cosθ 0 sinθ]
[0 1 0]
[-sinθ 0 cosθ]

Question 18

What is the 3x3 matrix for a rotation of θ° anticlockwise about the z axis?

Answer 18

[cosθ -sinθ 0]
[sinθ cosθ 0]
[0 0 1]