Chapter 7: Linear Transformations Flashcards
Where do linear transformations always map the origin onto?
Itself
What can linear transformations be represented by?
Matrices
What is the name given to points or lines that do not move, even when under the given transformation?
Invariant points/lines
What is the transformation matrix for a reflection in the y-axis?
|-1 0|
|0 1|
What is the transformation matrix for a reflection in the y-axis?
|1 0|
|0 -1|
What is the transformation matrix for a reflection in y=x?
|0 1|
|1 0|
What is the transformation matrix for a reflection in the y=-x?
|0 -1|
|-1 0|
What is the transformation matrix for rotation about the origin?
|cosθ -sinθ|
|sinθ cosθ|, θ being the angle taking anticlockwise.
What is the only invariant point in a rotation about the origin?
(0, 0)
What is the transformation for a stretch/enlargement?
|a 0|
|0 b|, a being the scale factor parallel to the x-axis and b being the scale factor parallel to the y-axis.
In what order is matrix PQ carried out?
Transformation Q, then transformation P
What is the transformation matrix for a reflection in the plane x=0?
|-1 0 0|
| 0 1 0|
| 0 0 1|
What is the transformation matrix for a reflection in the plane y=0?
1 0 0|
|0 -1 0|
| 0 0 1|
What is the transformation matrix for a reflection in the plane z=0?
1 0 0|
| 0 1 0|
|0 0 -1|
What is the transformation matrix for a rotation about the x-axis?
|1 0 0|
|0 cosθ -sinθ|
|0 sinθ cosθ|
