math111_logo Composition and Matrix Multiplication


Exercise Draw the picture and identify the composition TS.

1) T = Reflection in x-axis: R2R2
S = Reflection in y-axis: R2R2

Answer The composition TS is Reflection in origin: R2R2

2) T = Rotation by 90 degrees: R2R2
S = Reflection in origin: R2R2

Answer The composition TS is Rotation by -90 degrees: R2R2

3) T = Reflection in origin: R2R2
S = Rotation by 90 degrees: R2R2

Answer The composition TS is Rotation by -90 degrees: R2R2

4) T = Reflection in x-axis: R2R2
S = Embedding as diagonal: RR2

Answer The composition TS is Embedding as skew-diagonal: R2R2

5) T = Embedding as diagonal: RR2
S = Projection onto x-axis: R2R

Answer The composition TS is Vertical intersection with diagonal: R2R2

6) T = Projection onto x-axis: R2R
S = Embedding as diagonal: RR2

Answer The composition TS is the identity.