MAT2611 Assignment 10 2025 (Exceptionally Crafted) Due 22 August 2025

MAT2611
Assignment 10
Due 22 August 2025

, Student Name: MAT2611 Assignment 10


MAT2611 Assignment 10
Due: 22 August 2025



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: Write each map as a matrix.
   
4 0 −1 0 0  
    2 1 −1
[T1 ] = 1 −1 , [T2 ] =  0 0 0 , [T3 ] =  .
   
    0 2 3
2 −1 1 2 1


Step 2: Multiply [T2 ][T1 ].
    
−1 0 0 4 0 −4 0
    
[T2 ][T1 ] =  0 0 0 1 −1 =  0 0 .
    
    
1 2 1 2 −1 8 −3


Step 3: Multiply [T3 ] by the result.
 
  −4 0  
2 1 −1 
  −16 3
[T3 T2 T1 ] =  0 = .
 0 
0 2 3   24 −9
8 −3


Final Answer:
(T3 ◦ T2 ◦ T1 )(x, y) = (−16x + 3y, 24x − 9y).


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