MAT2611
Assignment 10
DUE 22 August 2025
, MAT2611
ASSIGNMENT 10
Due date: Friday,22 August 2025
Problem 1
To find (𝑇3 ∘ 𝑇2 ∘ 𝑇1 )(𝑥, 𝑦), compute the composition step by step.
First, apply 𝑇1 :
𝑇1 (𝑥, 𝑦) = (4𝑥, 𝑥 − 𝑦, 2𝑥 − 𝑦) .
Let 𝑢 = 4𝑥 , 𝑣 = 𝑥 − 𝑦 , 𝑤 = 2𝑥 − 𝑦 .
Next, apply 𝑇2 :
𝑇2 (𝑢, 𝑣, 𝑤) = (−𝑢, 0, 𝑢 + 2𝑣 + 𝑤)
= (−4𝑥, 0,4𝑥 + 2(𝑥 − 𝑦) + (2𝑥 − 𝑦))
= (−4𝑥, 0,4𝑥 + 2𝑥 − 2𝑦 + 2𝑥 − 𝑦)
= (−4𝑥, 0,8𝑥 − 3𝑦) .
Now, apply 𝑇3 :
𝑇3 (−4𝑥, 0,8𝑥 − 3𝑦) = (2(−4𝑥) + 0 − (8𝑥 − 3𝑦),2(0) + 3(8𝑥 − 3𝑦))
= (−8𝑥 − 8𝑥 + 3𝑦, 24𝑥 − 9𝑦)
= (−16𝑥 + 3𝑦, 24𝑥 − 9𝑦) .
Thus, (𝑇3 ∘ 𝑇2 ∘ 𝑇1 )(𝑥, 𝑦) = (−16𝑥 + 3𝑦, 24𝑥 − 9𝑦) .
Problem 2
Assignment 10
DUE 22 August 2025
, MAT2611
ASSIGNMENT 10
Due date: Friday,22 August 2025
Problem 1
To find (𝑇3 ∘ 𝑇2 ∘ 𝑇1 )(𝑥, 𝑦), compute the composition step by step.
First, apply 𝑇1 :
𝑇1 (𝑥, 𝑦) = (4𝑥, 𝑥 − 𝑦, 2𝑥 − 𝑦) .
Let 𝑢 = 4𝑥 , 𝑣 = 𝑥 − 𝑦 , 𝑤 = 2𝑥 − 𝑦 .
Next, apply 𝑇2 :
𝑇2 (𝑢, 𝑣, 𝑤) = (−𝑢, 0, 𝑢 + 2𝑣 + 𝑤)
= (−4𝑥, 0,4𝑥 + 2(𝑥 − 𝑦) + (2𝑥 − 𝑦))
= (−4𝑥, 0,4𝑥 + 2𝑥 − 2𝑦 + 2𝑥 − 𝑦)
= (−4𝑥, 0,8𝑥 − 3𝑦) .
Now, apply 𝑇3 :
𝑇3 (−4𝑥, 0,8𝑥 − 3𝑦) = (2(−4𝑥) + 0 − (8𝑥 − 3𝑦),2(0) + 3(8𝑥 − 3𝑦))
= (−8𝑥 − 8𝑥 + 3𝑦, 24𝑥 − 9𝑦)
= (−16𝑥 + 3𝑦, 24𝑥 − 9𝑦) .
Thus, (𝑇3 ∘ 𝑇2 ∘ 𝑇1 )(𝑥, 𝑦) = (−16𝑥 + 3𝑦, 24𝑥 − 9𝑦) .
Problem 2
