MAT2611
Assignment 10
Due 22 August 2025
, MAT2611 Assignment 10 — Due: 22 August 2025
MAT2611 Assignment 10
Due Date: Due: 22 August 2025
Solutions to Assignment 10
Problem 1
Problem Statement: Find (T3 ◦ T2 ◦ T1 )(x, y), where
T1 (x, y) = (4x, x−y, 2x−y), T2 (x, y, z) = (−x, 0, x+2y+z), T3 (x, y, z) = (2x+y−z, 2y+3z).
Step 1: Apply T1 :
T1 (x, y) = (4x, x − y, 2x − y).
Step 2: Apply T2 :
T2 (4x, x − y, 2x − y) = (−4x, 0, 8x − 3y).
Step 3: Apply T3 :
T3 (−4x, 0, 8x − 3y) = (−16x + 3y, 24x − 9y).
Final Answer:
(T3 ◦ T2 ◦ T1 )(x, y) = (−16x + 3y, 24x − 9y).
—
Page 1
Assignment 10
Due 22 August 2025
, MAT2611 Assignment 10 — Due: 22 August 2025
MAT2611 Assignment 10
Due Date: Due: 22 August 2025
Solutions to Assignment 10
Problem 1
Problem Statement: Find (T3 ◦ T2 ◦ T1 )(x, y), where
T1 (x, y) = (4x, x−y, 2x−y), T2 (x, y, z) = (−x, 0, x+2y+z), T3 (x, y, z) = (2x+y−z, 2y+3z).
Step 1: Apply T1 :
T1 (x, y) = (4x, x − y, 2x − y).
Step 2: Apply T2 :
T2 (4x, x − y, 2x − y) = (−4x, 0, 8x − 3y).
Step 3: Apply T3 :
T3 (−4x, 0, 8x − 3y) = (−16x + 3y, 24x − 9y).
Final Answer:
(T3 ◦ T2 ◦ T1 )(x, y) = (−16x + 3y, 24x − 9y).
—
Page 1
