Matrix transformations

Question 1

Rotation, centre the origin, through 180 degrees

Answer 1

(-1 0)
(0 -1)

Question 2

Reflection in the line y=x

Answer 2

(0 1)
(1 0)

Question 3

Enlargement by scale factor x

Answer 3

(x 0)
(0 x)

Question 4

Reflection in the x-axis

Answer 4

(1 0)
(0 -1)

Question 5

Matrix which represents a rotation through the angle theta anticlockwise about the origin

Answer 5

(cosx -sinx)
(sinx cosx)

Question 6

Stretch SF m parallel to x axis

Answer 6

(m 0)
( 0 1)

Question 7

Stretch SF n parallel to y axis

Answer 7

(1 0)
(0 n)

Question 8

x-axis fixed shear

Answer 8

(1 k)
(0 1)

Question 9

y-axis fixed shear

Answer 9

(1 0)
(k 1)

Question 10

Reflection in the line y = -x

Answer 10

(0 -1)
(-1 0)

Question 11

3D unit vectors in order i, j, k (x, y, z)

Answer 11

(1) (0) (0)
(0) (1) (0)
(0) (0) (1)

Question 12

3D rotation theta about the x-axis

Answer 12

(1 0 0 )
(0 cosx -sinx)
(0 sinx cosx)

Question 13

3D rotation theta about the y axis

Answer 13

(cosx 0 sinx)
(0 1 0)
(-sinx 0 cosx)

Question 14

3D rotation theta about the z axis

Answer 14

(cosx -sinx 0)
(sinx cosx 0)
(0 0 1)

Question 15

Reflection in the y axis

Answer 15

(-1 0)
(0 1)