MAT1503
,Assignment 4
Semester 2
2023
, Question 1:
Given a square matrix A:
(1.1) Performing the operation (3):
R2 ← R2 - 2R1
E1 =
[1 0 0]
[0 1 -2]
[0 0 1]
Performing E1A:
B = E1A =
[2 -1 1] [1
3 -3]
[1 -3 k + 9]
To find values of k such that a33 = a233, we set them equal:
k + 14 = k + 9
5=0
Since there is no value of k that satisfies the equation, there are no values of k in the range
[-1, 0] that make a33 = a233.
(1.2) Performing the operation (3):
R1 ←→ R3
E2 =
[0 0 1]
[0 1 0]
[1 0 0]
Performing E2A:
C = E2A =
[1 -3 k + 14]
[3 1 -1]
[2 -1 1]
,Assignment 4
Semester 2
2023
, Question 1:
Given a square matrix A:
(1.1) Performing the operation (3):
R2 ← R2 - 2R1
E1 =
[1 0 0]
[0 1 -2]
[0 0 1]
Performing E1A:
B = E1A =
[2 -1 1] [1
3 -3]
[1 -3 k + 9]
To find values of k such that a33 = a233, we set them equal:
k + 14 = k + 9
5=0
Since there is no value of k that satisfies the equation, there are no values of k in the range
[-1, 0] that make a33 = a233.
(1.2) Performing the operation (3):
R1 ←→ R3
E2 =
[0 0 1]
[0 1 0]
[1 0 0]
Performing E2A:
C = E2A =
[1 -3 k + 14]
[3 1 -1]
[2 -1 1]
