Chapter 7- Linear transformations

Question 1

Linear transformation properties

Answer 1

Maps origin onto itself
Representable by a matrix

Question 2

Reflection in y axis

Answer 2

(-1 0)
(0 1)

Question 3

Reflection in x axis

Answer 3

(1 0)
(0 -1)

Question 4

Reflection y=x

Answer 4

(0 1)
(1 0)

Question 5

Reflection in y=-x

Answer 5

(0 -1)
(-1 0)

Question 6

Rotation angle θ anticlockwise about origin

Answer 6

(cosθ -sinθ)
(sinθ cosθ)

Question 7

Stretch of scale factor a along x axis and stretch of scale factor b along y axis

Answer 7

(a 0)
(0 b)

Question 8

What does detM for a matrix representing a linear transformation show?

Answer 8

The area scale factor

Question 9

Reflection in x=0 plane

Answer 9

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

Question 10

Reflection in y=0 plane

Answer 10

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

Question 11

Reflection in z=0 plane

Answer 11

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

Question 12

Rotation by θ about x axis

Answer 12

(1 0 0)
(0 cosθ -sinθ)
(0 sinθ cosθ)

Question 13

Rotation by θ about y axis

Answer 13

(cosθ 0 sinθ)
(0 1 0 )
(-sinθ 0 cosθ)

Question 14

Rotation by θ about z axis

Answer 14

(cosθ -sinθ 0)
(sinθ cosθ 0)
(0 0 1)