MAT2611 Assignment 6 2025 ANSWERS - Due 27 June 2025

MAT2611
ASSIGNMENT 6 2025
DUE 27 JUNE 2025

, MAT2611
ASSIGNMENT 06
Due date: Friday, 27 June 2025




Solution for Problem 1
(a) Standard Matrices for T1 and T2 ​ ​




The standard matrix for a linear transformation is found by applying it to the standard basis vectors e1 ​ = (1, 0, 0),
e2 = (0, 1, 0), e3 =
​
. ​




(0, 0, 1)

For T1 (x1 , x2 , x3 )
​ ​ ​ ​ = (x1 + x2 , x1 − x2 , x3 ):
​ ​
​ ​
​
​
​ ​
​ ​




T1 (e1 ) = T1 (1, 0, 0) = (1 + 0, 1 − 0, 0) = (1, 1, 0)
​ ​ ​




T1 (e2 ) = T1 (0, 1, 0) = (0 + 1, 0 − 1, 0) = (1, −1, 0)
​ ​ ​




T1 (e3 ) = T1 (0, 0, 1) = (0 + 0, 0 − 0, 1) = (0, 0, 1)
​ ​ ​




1 1 0
Standard matrix for T1 is 1 −1 0 . ​




0 0 1




​ ​ ​ ​ ​




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