MAT2611 Assignment 6 2025 Due 27 June 2025

MAT2611
ASSIGNMENT 06
Due date: Friday, 27 June 2025
(a) Standard Matrices for
and
T

1 T

2
The standard matrix for a linear transformation is found by applying it to the standard basis vectors
e
,

=1 (1, 0, 0)
,
.
e

=2 (0, 1, 0) e

=3
(0, 0, 1)
For
:
T

(x

, x

, x

) =
(x
1 1 2 3

+1 x
2 1 x

, x

−

, x

)
2 3

T
1 1 T

(e

) =

(1, 0, 0) =
(1 + 0, 1 − 0, 0) = (1, 1, 0)
1
T
1 2 T

(e

) =

(0, 1, 0) =
(0 + 1, 0 − 1, 0) = (1, −1, 0)
1
T
1 3 T

(e

) =

(0, 0, 1) =
(0 + 0, 0 − 0, 1) = (0, 0, 1)
1
T

1
1
1
0
1
−1
0
0
0
1
Solution for Problem 1
Standard matrix for
is
.